Question

operations for solving equations with the variable on both sides - item 35079
solve each equation.
2c - 4 = 3(4 - 2c)
c =
-4a + 9 = -2(4 + 5a) - 7
a =

Explanation:

Step1: Expand the right - hand side

For the equation \(2c - 4=3(4 - 2c)\), use the distributive property \(a(b - c)=ab - ac\). So \(3(4 - 2c)=12-6c\), and the equation becomes \(2c - 4 = 12-6c\).

Step2: Add \(6c\) to both sides

\(2c+6c - 4=12-6c + 6c\), which simplifies to \(8c-4 = 12\).

Step3: Add 4 to both sides

\(8c-4 + 4=12 + 4\), resulting in \(8c=16\).

Step4: Divide both sides by 8

\(\frac{8c}{8}=\frac{16}{8}\), so \(c = 2\).

For the equation \(-4a + 9=-2(4 + 5a)-7\):

Step1: Expand the right - hand side

Using the distributive property, \(-2(4 + 5a)=-8-10a\). The equation becomes \(-4a + 9=-8-10a-7\).

Step2: Combine like terms on the right - hand side

\(-8-7=-15\), so the equation is \(-4a + 9=-15-10a\).

Step3: Add \(10a\) to both sides

\(-4a+10a + 9=-15-10a+10a\), which simplifies to \(6a + 9=-15\).

Step4: Subtract 9 from both sides

\(6a+9 - 9=-15 - 9\), resulting in \(6a=-24\).

Step5: Divide both sides by 6

\(\frac{6a}{6}=\frac{-24}{6}\), so \(a=-4\).

Answer:

\(c = 2\)
\(a=-4\)