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