Question

Select all the possible solutions for 2x+7 is less than or equal to 3x-5

Answer 1

2x + 7 <= 3x - 5

Treat <= as an = sign unless you divide or multiply by a negative number.

2x + 12 <= 3x

x <= 12

The answer is all real numbers less than or equal to 12.

Answer 2

2x + 7 ≤ 3x - 5

Isolate the x. Subtract 3x and 7 from both sides

2x (-3x) + 7 (-7) ≤ 3x (-3x) - 5 (-7)

2x - 3x ≤ -5 - 7

Combine like terms

(2x - 3x) ≤ (-5 - 7)

-x ≤ -12

Isolate the x. Divide -1 from both sides. Remember that when dividing by a negative number, you must flip the sign.

(-x)/-1 ≤ (-12)/-1

x ≥ -12/-1

x ≥ 12

x ≥ 12 is your answer

~Rise Above the Ordinary