Question

1. \\(-0.9p + 3.2 = -1.7p\\) 6) \\(-14.3 = -1.4 - 3d\\) 7) \\(14.2 = 2(-5.8 + t)\\) 8) \\(-10.6 = \frac{m + 11.7}{0.5}\\)

Explanation:

Problem 5:

Step1: Isolate p terms

Add $1.7p$ to both sides:
$-0.9p + 1.7p + 3.2 = -1.7p + 1.7p$
$0.8p + 3.2 = 0$

Step2: Isolate the p term

Subtract 3.2 from both sides:
$0.8p + 3.2 - 3.2 = 0 - 3.2$
$0.8p = -3.2$

Step3: Solve for p

Divide by 0.8:
$p = \frac{-3.2}{0.8}$
$p = -4$

Problem 6:

Step1: Isolate d terms

Add 1.4 to both sides:
$-14.3 + 1.4 = -1.4 + 1.4 - 3d$
$-12.9 = -3d$

Step2: Solve for d

Divide by -3:
$d = \frac{-12.9}{-3}$
$d = 4.3$

Problem 7:

Step1: Divide both sides by 2

$\frac{14.2}{2} = \frac{2(-5.8 + t)}{2}$
$7.1 = -5.8 + t$

Step2: Solve for t

Add 5.8 to both sides:
$7.1 + 5.8 = -5.8 + 5.8 + t$
$t = 12.9$

Problem 8:

Step1: Eliminate denominator

Multiply both sides by 0.5:
$-10.6 \times 0.5 = \frac{m + 11.7}{0.5} \times 0.5$
$-5.3 = m + 11.7$

Step2: Solve for m

Subtract 11.7 from both sides:
$-5.3 - 11.7 = m + 11.7 - 11.7$
$m = -17$

Answer:

1. $p = -4$
2. $d = 4.3$
3. $t = 12.9$
4. $m = -17$