Simple Algebraic Equations Question 6

What is the value of $5x-3$, given the following equation?

$$\frac{2}{3}(15x-9)-2=15x-9$$

$\dfrac{1}{5}$

$\dfrac{3}{5}$

$-2$

$-5$

Approach 1

An inefficient, but safe way to do this problem would be to solve for $x$ (or directly $5x-3)$. $$\frac{2}{3}(15x-9)-2=15x-9$$ $$\frac{2}{3}(15x)-\frac{2}{3}(9)-2=15x-9 $$ $$10x-6-2=15x-9$$ $$10x-8=15x-9$$ $$1=5x$$

Subtract 3 from both sides to get to the answer directly

$$1=5x$$ $$1-3=5x-3$$ $$\boxed{-2}=5x-3 $$

Solve for $x$

$$1=5x$$ $$\frac{1}{5}=x$$

Substitute the value for $x$

$$5x-3$$ $$5\left(\frac{1}{5}\right) -3$$ $$ 1-3 = \boxed{-2}$$

Approach 2

Take note that $5x-3$ can be tripled to obtain $15x-9$. Additionally, the $15x-9$ expression is present at both sides of the equation.

$$\underbrace{\frac{2}{3}(15x-9)}_{\text{two-thirds of an expression}}-2=\underbrace{15x-9}_{\text{a whole of an expression}} $$

We can subtract two-thirds of $15x-9$ from both sides, which will result in one-thirds of the expression on the right side.

$$-2=\frac{1}{3}(15x-9)$$

Conveniently, a third of $15x-9$ is our desired final expression.

$$\boxed{-2}=5x-3$$