Solve Linear Equations in One Variable

What is the value of x in the equation 5(2x − 6) > 6 − 6(3x − 1)?

• x>0.4

• x<0.6

• x<1.5

• x>1.5

Four times a number plus fifteen is equal to two times that same number plus forty-five. What is the number?

• 5

• 10

• 15

• 30

Which statement is true about the equation 2(4x+10) = 8x+12?

• The equation has only one solution, x=8

• The equation has only one solution, x=-8

• The equation has no solution

• The equation has infinite solutions

Martina is solving the equation Here are the first steps of her solution.

4x – 11 = 2x + 391

4x = 2x + 402

2x = 402

What did Martina do to get 2x = 402?

• divided both sides by 2

• divided the left side by 2x

• subtracted 2x from both sides

• subtracted 2x from the left side and added 2x to the right side

What is the solution to the equation below?

4(3x + 5) = 5(x + 4) + 7x

• infinite solutions

• no solution

• 0

• 3/8

What is the solution to the equation

3–2(x + 1)=2(1–x)?

• x=-2

• x=2

• no solution

• infinitely many solutions

Company X uses the equation c = 10t + 40 to determine the cost (c) of a project given the time (t) it takes to complete the project. Company Y uses the equation c = 20t to determine the cost of a project given the amount of time it takes to complete the project. How many hours would a project take that costs the same for both companies?

• 1.75 hours

• 4 hours

• 5 hours

• 30 hours

Robert bought new carpet for his living room. The store charged a flat rate of $300.00 to remove the old carpet and install the new carpet. Robert paid $2.79 per square foot for carpet. Before taxes, Robert paid a total of $1,262.55 for carpet. How many square feet of carpet did Robert purchase?

• 153 square feet

• 345 square feet

• 452 square feet

• 560 square feet

What is the solution to the equation

3y + 7(5y –4) + 10 = 6(y – 3) + 32y?

• infinite solutions

• no solution

• y = ⁹/₁₉

• y = 0

What is the value of x in the equation?

• -⁵/₈

• -¹/₈

• ¹/₈

• ⁵/₈