Question

1. $5(6 + 3x) + 7 \geq 127$
2. $-1 - 6x - 6 > -11 - 7x$

Explanation:

Step1: Expand left side (Q10)

$5(6+3r)+7 = 30 + 15r + 7$

Step2: Simplify left side (Q10)

$30 + 15r + 7 = 37 + 15r$

Step3: Isolate variable term (Q10)

$37 + 15r \geq 127 \implies 15r \geq 127 - 37$

Step4: Solve for r (Q10)

$15r \geq 90 \implies r \geq \frac{90}{15} = 6$

Step5: Combine constants (Q12)

$-1 -6x -6 = -7 -6x$

Step6: Isolate variable terms (Q12)

$-7 -6x > -11 -7x \implies -6x +7x > -11 +7$

Step7: Solve for x (Q12)

$x > -4$

Answer:

1. $r \geq 6$ (On the number line, plot a closed dot at 6 and shade to the right)
2. $x > -4$ (On the number line, plot an open dot at -4 and shade to the right)