## Multi-Step Linear Equation:

• A linear equation of one variable is an equation in terms of only one variable of degree 1.
• The value of the variable which satisfies the equation is called the solution of the equation.
• A multi-step linear equation is a linear equation that can be solved using multiple algebraic operations on both sides of the equation.

Let us assume the number of pounds of {eq}\$7 {/eq} coffee is {eq}x {/eq}. This is mixed with {eq}10 {/eq} pounds of {eq}\$ 3 {/eq} coffee.

The result is {eq}(10+x) {/eq} pounds of {eq}\\$ 5 {/eq} coffee.

So we get the equation:

$$7(x)+ 3(10) = 5 (x+10)\\[0.4cm] 7x+30 = 5x+50 \\[0.4cm] \text{Subtracting 5x from both sides},\\[0.4cm] 2x+30=50\\[0.4cm] \text{Subtracting 30 from both sides},\\[0.4cm] 2x=20\\[0.4cm] \text{Dividing both sides by 2},\\[0.4cm] x= \color{blue}{\boxed{\mathbf{10 \text{ pounds}}}}$$