Question

pa: solving one - step equations

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

Substitute \(x=-6\) into \(\frac{2}{1}x=-12\) (assuming the fraction is \(\frac{2}{1}\), if it's \(\frac{2}{3}\) etc. the following will change accordingly). We get \(2\times(-6)\).
\[2\times(-6)=-12\]

Step2: Check the equality

The left - hand side \(2\times(-6)=-12\), and the right - hand side is \(-12\). Since the left - hand side equals the right - hand side, \(-6\) is a solution.

Step1: Substitute \(g=-5\) into the equation

We have the equation \(w + g=-8\), substituting \(g = - 5\) gives \(w+(-5)=-8\).
\[w-5=-8\]

Step2: Solve for \(w\)

Add 5 to both sides of the equation \(w-5 + 5=-8 + 5\).
\[w=-3\]

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: Add \(\frac{5}{3}\) to both sides

\(h=\frac{11}{2}+\frac{5}{3}\). Find a common denominator, which is 6. So \(\frac{11}{2}\times\frac{3}{3}=\frac{33}{6}\) and \(\frac{5}{3}\times\frac{2}{2}=\frac{10}{6}\). Then \(h=\frac{33 + 10}{6}=\frac{43}{6}=7\frac{1}{6}\).

Answer:

Yes, \(-6\) is a solution to the equation.

For the second equation (it seems to be \(w + g=-8\) and the work shows \(g = - 5\), but the question is not clear. Assuming we want to solve for \(w\) given \(g=-5\)):