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Problem 188

# Solve for $$x: 2 x+5 x=7-x$$

Expert verified
The solution to the equation $$2x + 5x = 7 - x$$ is $$x = \frac{7}{8}$$.
See the step by step solution

## Step 1: Combine like terms on both sides of the equation

Combine the $$x$$ terms on both sides of the equation. On the left side, we have $$2x + 5x$$, and on the right side, we have $$7 - x$$.

## Step 2: Add $$x$$ to both sides

First, we need to isolate $$x$$. We do this by adding $$x$$ to both sides of the equation: $(2x + 5x) + x = 7 - x + x$

## Step 3: Simplify both sides

Now, we can add the $$x$$ terms on both sides of the equation. On the left side, we have $$2x + 5x + x = 8x$$, and on the right side, we have $$7 - x + x = 7$$: $8x = 7$

## Step 4: Isolate $$x$$

Now we need to isolate $$x$$. To do this, we will divide both sides of the equation by $$8$$: $\frac{8x}{8} = \frac{7}{8}$

## Step 5: Solve for $$x$$

Finally, we can finish solving the equation. Since $$\frac{8x}{8}$$ is simply $$x$$, we find that: $x = \frac{7}{8}$ So the solution to the equation $$2x + 5x = 7 - x$$ is $$x = \frac{7}{8}$$.

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