To solve the equation:
[tex]\[ 4(x - 2) + 18 = \frac{1}{2} x + 10 \][/tex]
we follow these steps:
1. Distribute the 4 inside the parentheses:
[tex]\[ 4(x - 2) + 18 = \frac{1}{2} x + 10 \][/tex]
becomes
[tex]\[ 4x - 8 + 18 = \frac{1}{2} x + 10 \][/tex]
2. Combine like terms on the left-hand side:
[tex]\[ 4x - 8 + 18 = 4x + 10 \][/tex]
becomes
[tex]\[ 4x + 10 = \frac{1}{2} x + 10 \][/tex]
3. Move all terms involving [tex]\( x \)[/tex] to one side and constants to the other side. First, subtract [tex]\( \frac{1}{2} x \)[/tex] from both sides to move the [tex]\( x \)[/tex] terms together:
[tex]\[ 4x - \frac{1}{2} x = 10 - 10 \][/tex]
4. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ \frac{8}{2}x - \frac{1}{2} x = 0 \][/tex]
[tex]\[ \frac{7}{2} x = 0 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 0 \][/tex]
So, the solution to the equation is:
[tex]\[ x = 0 \][/tex]
