how to simplify and solve
2/5(20x+5)-1/2(8-4x)=38
1. find a common multiple for the denominators of both fractions.
2. combine the fractions together. do not expand the numerator first.
3. cross multiply.
4. expand the terms
5. make x the subject.
6. solve.
Here is a better way.
Perform the indicated multiplications and combine terms
(2/5)(20x+5) - (1/2)(8-4x) = 38
8x +2 -4 +2x = 38
10x = 40
x = 4
To solve the equation 2/5(20x+5)-1/2(8-4x)=38, we need to simplify and then isolate the variable x.
Step 1: Simplify the equation.
Let's first simplify the expressions within the parentheses:
2/5(20x+5) = (2/5)*(20x+5) = 8x + 2
1/2(8-4x) = (1/2)*(8-4x) = 4 - 2x
Now, substituting these simplified expressions back into the equation, we have:
8x + 2 - (4 - 2x) = 38
Step 2: Remove the parentheses.
Distribute the negative sign across (4 - 2x) to eliminate the parentheses:
8x + 2 - 4 + 2x = 38
Combine like terms:
10x - 2 = 38
Step 3: Isolate the variable x.
Add 2 to both sides of the equation to isolate the variable term:
10x - 2 + 2 = 38 + 2
10x = 40
Finally, divide both sides of the equation by 10 to solve for x:
10x/10 = 40/10
x = 4
Therefore, the solution to the equation 2/5(20x+5)-1/2(8-4x)=38 is x = 4.