Question

2 numeric 1 point
the variable $x$ is a positive integer. if $3(x - 1) + 5 > 11$ and $-5x + 18 \geq -12$, how many possible values are there for $x$?
answer

Explanation:

Step1: Solve first inequality

Start with $3(x - 1) + 5 > 11$.
Expand: $3x - 3 + 5 > 11$
Simplify: $3x + 2 > 11$
Subtract 2: $3x > 9$
Divide by 3: $x > 3$

Step2: Solve second inequality

Start with $-5x + 18 \geq -12$.
Subtract 18: $-5x \geq -30$
Divide by -5 (reverse inequality): $x \leq 6$

Step3: Find positive integer x values

Combine inequalities: $3 < x \leq 6$.
Positive integers: 4, 5, 6.

Answer:

3