Question

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. $h - 1\frac{2}{3}=5\frac{1}{2}$

Explanation:

1. Is -6 a solution to the equation: $\frac{2}{3}x=-12$?

Step1: Substitute $x = - 6$ into the equation

Substitute $x=-6$ into $\frac{2}{3}x$. We get $\frac{2}{3}\times(-6)$.

Step2: Calculate the result

$\frac{2}{3}\times(-6)=2\times(-2)= - 4$. Since $-4
eq - 12$, -6 is not a solution.

2. Solve the equation $-3 + g=-8$

Step1: Isolate the variable $g$

Add 3 to both sides of the equation $-3 + g=-8$. We have $g=-8 + 3$.

Step2: Calculate the value of $g$

$-8+3=-5$, so $g = - 5$.

3. Solve the equation $h-1\frac{2}{3}=5\frac{1}{2}$

Step1: Convert mixed - numbers to improper fractions

$1\frac{2}{3}=\frac{1\times3 + 2}{3}=\frac{5}{3}$ and $5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}$. The equation becomes $h-\frac{5}{3}=\frac{11}{2}$.

Step2: Isolate the variable $h$

Add $\frac{5}{3}$ to both sides: $h=\frac{11}{2}+\frac{5}{3}$.

Step3: Find a common denominator and add

The common denominator of 2 and 3 is 6. $\frac{11}{2}+\frac{5}{3}=\frac{11\times3}{2\times3}+\frac{5\times2}{3\times2}=\frac{33}{6}+\frac{10}{6}=\frac{33 + 10}{6}=\frac{43}{6}=7\frac{1}{6}$. So $h = 7\frac{1}{6}$.

Answer:

No