Answer :
Let's solve the given equations step-by-step:
[tex]\frac{1}{2}x + 2.9 = 36.9[/tex]
We need to solve for [tex]x[/tex].
Step 1: Subtract 2.9 from both sides
[tex]\frac{1}{2}x + 2.9 - 2.9 = 36.9 - 2.9[/tex]
[tex]\frac{1}{2}x = 34[/tex]Step 2: Multiply both sides by 2 to solve for [tex]x[/tex]
[tex]x = 34 \times 2[/tex]
[tex]x = 68[/tex]So, the solution to the first equation is [tex]x = 68[/tex].
[tex]5.6x - 2.4x = 4[/tex]
We need to simplify and solve for [tex]x[/tex].
Step 1: Combine like terms on the left side
[tex](5.6 - 2.4)x = 4[/tex]
[tex]3.2x = 4[/tex]Step 2: Divide both sides by 3.2 to solve for [tex]x[/tex]
[tex]x = \frac{4}{3.2}[/tex]
[tex]x = 1.25[/tex]So, the solution to the second equation is [tex]x = 1.25[/tex].
This question involves solving linear equations, a fundamental part of high school algebra. The solutions involve basic operations like addition, subtraction, multiplication, and division to isolate the variable [tex]x[/tex].