Question 561·Medium·Algebra

The distributive property sends $4$ to both $2x$ and $5$, and $7$ to both $x$ and $-2$. The outside number multiplies every term inside the parentheses. Distribute on both sides:

The negative term matters: $7(-2)=-14$, not $-2$.

Type the original equation as $4(2x_1+5)-3x_1\sim7(x_1-2)+10$. Desmos treats $x_1$ as the value to find, and $\sim$ tells its regression to make the sides equal. Under PARAMETERS, it shows $x_1=12$. So the requested value of $x$ is $12$. Grid in 12.

Start with the distributed equation. Combine the like terms $8x$ and $-3x$, which both have an $x$:

Their coefficients combine to make $5x$.

Combine the constants, the numbers without $x$:

Keep the negative sign on $-14$ when adding $10$.

Subtract $5x$ from both sides to keep them equal:

Add $4$ to both sides:

Divide both sides by $2$:

So the value of $x$ is $12$. Grid in 12.