Exam 1: Equations and Inequalities

Solve the problem. -A 11 m by 16 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $456 \mathrm {~m} ^ { 2 } ?$

(Multiple Choice)

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Question 221

Solve the equation. - $\frac { - 5 } { x - 3 } + \frac { 3 } { x + 3 } = \frac { - 30 } { x ^ { 2 } - 9 }$

(Multiple Choice)

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Question 222

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 8 ( x - 1 ) + ( 14 x ) = 6 ( x - 9 ) - 14$

(Multiple Choice)

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Question 223

Solve for y. - $7 x + 10 y = 7$

(Multiple Choice)

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Question 224

Write the inequality in interval notation. -

(Multiple Choice)

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Question 225

Solve the equation. - $\sqrt { 6 x - 5 } - \sqrt { 4 x + 8 } = 0$

(Multiple Choice)

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Question 226

Solve the equation. - $\frac { x + 16 } { 7 } = \frac { 4 x - 5 } { x }$

(Multiple Choice)

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Question 227

Solve the problem. -In a milling operation, the thickness of the aluminium foil that can be produced satisfies the inequality $| x - 1.94 | \leq 1.02$ . What range of thicknesses corresponds to this inequality?

(Multiple Choice)

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Question 228

Solve the equation by the zero-factor property. - $x ^ { 2 } - 4 x - 32 = 0$

(Multiple Choice)

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Question 229

Solve the inequality. Write the solution set in interval notation. - $( x + 10 ) ( x - 9 ) ( x - 10 ) > 0$

(Multiple Choice)

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Question 230

Solve the problem. -A boat is 144 feet from the base of cliff. If the distance from the top of the cliff to the boat is 36 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a Foot if necessary.

(Multiple Choice)

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Question 231

Write the inequality in interval notation. - $x > - 1$

(Multiple Choice)

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Question 232

Solve the equation. - $| 8 x + 7 | = | x + 4 |$

(Multiple Choice)

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Question 233

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { m } ^ { 3 }$ and a radius of $11 \mathrm {~m}$ . Find the height of the container.

(Multiple Choice)

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Question 234

Write the inequality in interval notation. - $- 8 < \mathrm { x } < 2$

(Multiple Choice)

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Question 235

Solve the inequality. Write the solution set in interval notation. - $| 5 x + 7 | < 14$

(Multiple Choice)

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Question 236

Write the statement as an absolute value inequality. - $m$ is no more than 9 units from 6

(Multiple Choice)

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Question 237

Solve the equation by the zero-factor property. - $8 x ^ { 2 } + 2 x - 6 = 0$

(Multiple Choice)

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Question 238

Solve the inequality. Write the solution set in interval notation. - $( x + 5 ) ( x + 4 ) ( x + 1 ) > 0$

(Multiple Choice)

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Question 239

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 8 } } { \sqrt { 72 } }$

(Multiple Choice)

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Question 240

Solve the problem. -A 11 m by 16 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $456 \mathrm {~m} ^ { 2 } ?$

Solve the equation. - $\frac { - 5 } { x - 3 } + \frac { 3 } { x + 3 } = \frac { - 30 } { x ^ { 2 } - 9 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 8 ( x - 1 ) + ( 14 x ) = 6 ( x - 9 ) - 14$

Solve for y. - $7 x + 10 y = 7$

Write the inequality in interval notation. -

Solve the equation. - $\sqrt { 6 x - 5 } - \sqrt { 4 x + 8 } = 0$

Solve the equation. - $\frac { x + 16 } { 7 } = \frac { 4 x - 5 } { x }$

Solve the problem. -In a milling operation, the thickness of the aluminium foil that can be produced satisfies the inequality $| x - 1.94 | \leq 1.02$ . What range of thicknesses corresponds to this inequality?

Solve the equation by the zero-factor property. - $x ^ { 2 } - 4 x - 32 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 10 ) ( x - 9 ) ( x - 10 ) > 0$

Solve the problem. -A boat is 144 feet from the base of cliff. If the distance from the top of the cliff to the boat is 36 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a Foot if necessary.

Write the inequality in interval notation. - $x > - 1$

Solve the equation. - $| 8 x + 7 | = | x + 4 |$

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { m } ^ { 3 }$ and a radius of $11 \mathrm {~m}$ . Find the height of the container.

Write the inequality in interval notation. - $- 8 < \mathrm { x } < 2$

Solve the inequality. Write the solution set in interval notation. - $| 5 x + 7 | < 14$

Write the statement as an absolute value inequality. - $m$ is no more than 9 units from 6

Solve the equation by the zero-factor property. - $8 x ^ { 2 } + 2 x - 6 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 5 ) ( x + 4 ) ( x + 1 ) > 0$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 8 } } { \sqrt { 72 } }$

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the problem. -A 11 m by 16 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 456 m2?456 \mathrm {~m} ^ { 2 } ?456 m2?

Solve the equation. - −5x−3+3x+3=−30x2−9\frac { - 5 } { x - 3 } + \frac { 3 } { x + 3 } = \frac { - 30 } { x ^ { 2 } - 9 }x−3−5​+x+33​=x2−9−30​

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - −8(x−1)+(14x)=6(x−9)−14- 8 ( x - 1 ) + ( 14 x ) = 6 ( x - 9 ) - 14−8(x−1)+(14x)=6(x−9)−14

Solve for y. - 7x+10y=77 x + 10 y = 77x+10y=7

Write the inequality in interval notation. -

Solve the equation. - 6x−5−4x+8=0\sqrt { 6 x - 5 } - \sqrt { 4 x + 8 } = 06x−5​−4x+8​=0

Solve the equation. - x+167=4x−5x\frac { x + 16 } { 7 } = \frac { 4 x - 5 } { x }7x+16​=x4x−5​

Solve the problem. -In a milling operation, the thickness of the aluminium foil that can be produced satisfies the inequality ∣x−1.94∣≤1.02| x - 1.94 | \leq 1.02∣x−1.94∣≤1.02 . What range of thicknesses corresponds to this inequality?

Solve the equation by the zero-factor property. - x2−4x−32=0x ^ { 2 } - 4 x - 32 = 0x2−4x−32=0

Solve the inequality. Write the solution set in interval notation. - (x+10)(x−9)(x−10)>0( x + 10 ) ( x - 9 ) ( x - 10 ) > 0(x+10)(x−9)(x−10)>0

Solve the problem. -A boat is 144 feet from the base of cliff. If the distance from the top of the cliff to the boat is 36 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a Foot if necessary.

Write the inequality in interval notation. - x>−1x > - 1x>−1

Solve the equation. - ∣8x+7∣=∣x+4∣| 8 x + 7 | = | x + 4 |∣8x+7∣=∣x+4∣

Solve the problem. -A cylindrical container has a volume of 1936πm31936 \pi \mathrm { m } ^ { 3 }1936πm3 and a radius of 11 m11 \mathrm {~m}11 m . Find the height of the container.

Write the inequality in interval notation. - −8<x<2- 8 < \mathrm { x } < 2−8<x<2

Solve the inequality. Write the solution set in interval notation. - ∣5x+7∣<14| 5 x + 7 | < 14∣5x+7∣<14

Write the statement as an absolute value inequality. - mmm is no more than 9 units from 6

Solve the equation by the zero-factor property. - 8x2+2x−6=08 x ^ { 2 } + 2 x - 6 = 08x2+2x−6=0

Solve the inequality. Write the solution set in interval notation. - (x+5)(x+4)(x+1)>0( x + 5 ) ( x + 4 ) ( x + 1 ) > 0(x+5)(x+4)(x+1)>0

Multiply or divide, as indicated. Simplify the answer. - −872\frac { \sqrt { - 8 } } { \sqrt { 72 } }72​−8​​

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Solve the problem. -A 11 m by 16 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $456 \mathrm {~m} ^ { 2 } ?$

Solve the equation. - $\frac { - 5 } { x - 3 } + \frac { 3 } { x + 3 } = \frac { - 30 } { x ^ { 2 } - 9 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 8 ( x - 1 ) + ( 14 x ) = 6 ( x - 9 ) - 14$

Solve for y. - $7 x + 10 y = 7$

Solve the equation. - $\sqrt { 6 x - 5 } - \sqrt { 4 x + 8 } = 0$

Solve the equation. - $\frac { x + 16 } { 7 } = \frac { 4 x - 5 } { x }$

Solve the problem. -In a milling operation, the thickness of the aluminium foil that can be produced satisfies the inequality $| x - 1.94 | \leq 1.02$ . What range of thicknesses corresponds to this inequality?

Solve the equation by the zero-factor property. - $x ^ { 2 } - 4 x - 32 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 10 ) ( x - 9 ) ( x - 10 ) > 0$

Write the inequality in interval notation. - $x > - 1$

Solve the equation. - $| 8 x + 7 | = | x + 4 |$

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { m } ^ { 3 }$ and a radius of $11 \mathrm {~m}$ . Find the height of the container.

Write the inequality in interval notation. - $- 8 < \mathrm { x } < 2$

Solve the inequality. Write the solution set in interval notation. - $| 5 x + 7 | < 14$

Write the statement as an absolute value inequality. - $m$ is no more than 9 units from 6

Solve the equation by the zero-factor property. - $8 x ^ { 2 } + 2 x - 6 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 5 ) ( x + 4 ) ( x + 1 ) > 0$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 8 } } { \sqrt { 72 } }$