Question

pa: solving one - step equations

1. is - 6 a solution to the equation: $\frac{2}{3}x=-12$? show work to justify your answer.

solve the following equations.

1. $-3 + g=-8$
2. $h - 1\frac{2}{3}=5\frac{1}{2}$
3. $-\frac{w}{6}=-5$
4. $-\frac{2}{5}x = 4$

Explanation:

Step1: Check if -6 is a solution for $\frac{2}{3}x=-12$

Substitute $x = - 6$ into the equation: $\frac{2}{3}\times(-6)=-4
eq - 12$. So -6 is not a solution.

Step2: Solve $-3 + g=-8$

Add 3 to both sides: $g=-8 + 3=-5$.

Step3: Solve $h-1\frac{2}{3}=5\frac{1}{2}$

Convert mixed - numbers to improper fractions: $h-\frac{5}{3}=\frac{11}{2}$. Add $\frac{5}{3}$ to both sides. $h=\frac{11}{2}+\frac{5}{3}=\frac{33 + 10}{6}=\frac{43}{6}=7\frac{1}{6}$.

Step4: Solve $-\frac{w}{6}=-5$

Multiply both sides by - 6: $w=(-5)\times(-6)=30$.

Step5: Solve $-\frac{2}{5}x = 4$

Multiply both sides by $-\frac{5}{2}$: $x=4\times(-\frac{5}{2})=-10$.

Answer:

1. No
2. $g=- 5$
3. $h = 7\frac{1}{6}$
4. $w = 30$
5. $x=-10$