Keystone Test Algebra: Linear Equations/Inequalities 2

Question 1

A gym charges a $30 registration fee plus $25 per month. If a member spent a total of $205, how many months did they pay for?

Accepted Answer

7

Answer

Set up 30 + 25m = 205; subtract 30 to get 25m = 175, so m = 7.

Question 2

Which value of x satisfies 4(x − 3) = 2x + 6?

Accepted Answer

9

Answer

Distribute to get 4x − 12 = 2x + 6; subtract 2x and add 12 to get 2x = 18, so x = 9.

Question 3

What is the solution to the inequality 3x + 7 ≥ 22?

Accepted Answer

x ≥ 5

Answer

Subtract 7 from both sides: 3x ≥ 15, then divide by 3: x ≥ 5.

Question 4

A line passes through (0, −4) and has a slope of 3. What is the equation of the line?

Accepted Answer

y = 3x − 4

Answer

Using slope-intercept form y = mx + b with m = 3 and b = −4 gives y = 3x − 4.

Question 5

If 2(y + 5) − 3y = 1, what is the value of y?

Accepted Answer

9

Answer

Distribute: 2y + 10 − 3y = 1; combine: −y + 10 = 1; so −y = −9, giving y = 9.

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