How do you solve #0.8x - ( 0.7x + 0.36) = 7.1#?

Question

Eva Adamson · Accepted Answer

undefined To solve the equation $0.8x - (0.7x + 0.36) = 7.1$, you need to simplify the expression by first distributing the negative sign within the parentheses and then combining like terms. After simplifying, isolate $x$ by performing the necessary arithmetic operations.

Here are the steps:

1. Distribute the negative sign:

$0.8x - 0.7x - 0.36 = 7.1$

2. Combine like terms:

$0.8x - 0.7x$ becomes $0.1x$

So, the equation becomes:

$0.1x - 0.36 = 7.1$

3. Add $0.36$ to both sides to isolate $0.1x$:

$0.1x = 7.1 + 0.36$

$0.1x = 7.46$

4. To solve for $x$, divide both sides by $0.1$:

$x = \frac{7.46}{0.1}$

$x = 74.6$

So, the solution to the equation $0.8x - (0.7x + 0.36) = 7.1$ is $x = 74.6$.

Isaiah Anthony · Answer

See a solution process below:

First expand the terms in parenthesis on the left side of the equation by removing the parenthesis and combining like terms. Be careful to get the signs of each term correct: #0.8x - 0.7x - 0.36 = 7.1# #(0.8x - 0.7)x - 0.36 = 7.1# #0.1x - 0.36 = 7.1# Next, add #color(red)(0.36)# to each side of the equation to isolate the #x# term while keeping the equation balanced: #0.1x - 0.36 + color(red)(0.36) = 7.1 + color(red)(0.36)# #0.1x - 0 = 7.46# #0.1x = 7.46# Now, divide each side of the equation by #color(red)(0.1)# to solve for #x# while keeping the equation balanced: #(0.1x)/color(red)(0.1) = 7.46/color(red)(0.1)# #(color(red)(cancel(color(black)(0.1)))x)/cancel(color(red)(0.1)) = 74.6# #x = 74.6#