SAT Linear Equations And Inequalities Practice Questions (Free + Explanations)

Algebra · Linear Equations And Inequalities

SAT Linear Equations And Inequalities Practice Questions (Free + Explanations) | Quiz 5

Question 12345 of 5

Question 1 of 5

A bike rental company charges a one-time delivery fee and a fixed cost per hour. The graph of the total cost versus the number of hours rented is a line that crosses the cost axis at 12 and passes through the point (4, 30) . Which equation represents the total cost C in dollars after renting a bike for h hours?

Explanation The line crosses the cost axis at 12, so the y -intercept is 12 . That means the equation has the form C = mh + 12 . Since the line passes through (4, 30), substitute h = 4 and C = 30 : 30 = 4 m + 12 18 = 4 m m = 4.5 So the equation is C = 4.5 h + 12. Concept summary For a linear model in context, use the intercept as the starting value and compute the slope from the change in output over the change in input.

Question 2 of 5

For all values of x except x = 4, the expression \frac{3 x - 12}{x - 4} is equivalent to which of the following?

Explanation Factor the numerator: 3 x - 12 = 3 (x - 4) . Then the expression becomes \frac{3 ( x - 4 )}{x - 4} . For any value of x such that x \neq = 4, the factor x - 4 cancels, leaving 3. So the equivalent expression is 3 . Concept summary To find an equivalent form of a rational expression, factor first and then cancel only common factors that appear in both the numerator and denominator.

Question 3 of 5

In the x y -plane, a line passes through the points (2, 7) and (8, 1) . Which equation represents this line?

Explanation First find the slope using the two points: m = \frac{1 - 7}{8 - 2} = \frac{- 6}{6} = - 1 So the equation has the form y = - x + b . Substitute one of the points, such as (2, 7) : 7 = - 2 + b b = 9 Therefore, the equation of the line is y = - x + 9 Concept summary To write an equation from two points, find the slope from the graph or coordinates, then use one point to determine the y -intercept.

Question 4 of 5

For the system {2 x + y = 11 3 x - 2 y = k the solution is (3, 5) . What is the value of k ?

Explanation Because (3, 5) is the solution to the system, it must satisfy both equations. Check the second equation: 3 x - 2 y = k Substitute x = 3 and y = 5 : 3 (3) - 2 (5) = 9 - 10 = - 1 So k = - 1 . Concept summary In a system of equations, an ordered pair is a solution only if it makes each equation true. Substitute the given coordinates into the equation containing the unknown parameter.

Question 5 of 5

For all values of x that satisfy 3 (x - 4) + 5 \leq 2 x + 9, which of the following is an equivalent solution set?

Explanation Start by simplifying the inequality: 3 (x - 4) + 5 \leq 2 x + 9 Distribute the 3 : 3 x - 12 + 5 \leq 2 x + 9 Combine like terms: 3 x - 7 \leq 2 x + 9 Subtract 2 x from both sides: x - 7 \leq 9 Add 7 to both sides: x \leq 16 So the equivalent solution set is x \leq 16 . Concept summary To solve a linear inequality, distribute first, combine like terms, then isolate the variable using the same operations as with an equation. Reverse the inequality sign only when multiplying or dividing by a negative number.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

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Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. A bike rental company charges a one-time delivery fee and a fixed cost per hour. The graph of the total cost versus the number of hours rented is a line that crosses the cost axis at 12 and passes through the point ( 4 , 30 ) . Which equation represents the total cost C in dollars after renting a bike for h hours?

Q2. For all values of x except x = 4 , the expression x − 4 3 x − 12  is equivalent to which of the following?

Q3. In the x y -plane, a line passes through the points ( 2 , 7 ) and ( 8 , 1 ) . Which equation represents this line?

Q4. For the system { 2 x + y = 11 3 x − 2 y = k  the solution is ( 3 , 5 ) . What is the value of k ?

Q5. For all values of x that satisfy 3 ( x − 4 ) + 5 ≤ 2 x + 9 , which of the following is an equivalent solution set?