Question

if hj = 7x - 27, find the value of x.
3x - 5 x - 1
h i j

Explanation:

Step1: Set up equation

Since $HJ=HI + IJ$, we have $7x - 27=(3x - 5)+(x - 1)$.

Step2: Simplify right - hand side

$(3x - 5)+(x - 1)=3x - 5+x - 1=4x-6$. So the equation becomes $7x - 27 = 4x-6$.

Step3: Move terms with $x$ to one side

Subtract $4x$ from both sides: $7x-4x - 27=4x-4x - 6$, which simplifies to $3x-27=-6$.

Step4: Isolate the variable term

Add 27 to both sides: $3x-27 + 27=-6 + 27$, getting $3x=21$.

Step5: Solve for $x$

Divide both sides by 3: $\frac{3x}{3}=\frac{21}{3}$, so $x = 7$.

Answer:

$x = 8$