Question

9 solve for x and identify the number of solutions. use paper to record your work.
3x + 5 = 2x - 1 + x

10 solve for x and identify the number of solutions. use paper to record your work.
-14x + 2 + x = 7 - 13x - 5

11 rewrite \six less than five times x\ as an expression using math symbols only

Explanation:

Problem 9

Step1: Simplify right side

Combine like terms: \(2x + x = 3x\), so equation becomes \(3x + 5 = 3x - 1\).

Step2: Subtract \(3x\) from both sides

\(3x - 3x + 5 = 3x - 3x - 1\) → \(5 = -1\).

Step1: Simplify both sides

Left: \(-14x + x + 2 = -13x + 2\); Right: \(7 - 5 - 13x = 2 - 13x\). Equation: \(-13x + 2 = -13x + 2\).

Step2: Add \(13x\) to both sides

\(-13x + 13x + 2 = -13x + 13x + 2\) → \(2 = 2\).

"Five times \(x\)" is \(5x\), "six less than" means subtract 6. So expression is \(5x - 6\).

Answer:

No solution (since \(5 = -1\) is false).

Problem 10