Question

Solve the following linear equations
$3x + 5 = 8 \\ 4x - 7 = 13 \\ 3(x - 2) = 15 \\ 3(x + 7) = 18$
​

Answer 1

(i) $3x+5=8$

Let's solve your equation step-by-step.

$3x+5=8$

Step 1: Subtract 5 from both sides.

$3x+5-5=8-5$

$3x=3$

Step 2: Divide both sides by 3.

$\frac{3x}{3} =\frac{3}{3}$

$x=1$

Let's verify is $\bf \underline{x=1}$

$3x+5=8$

$(3\times 1)+5=8$

$3+5=8$

$8=8$

$\bf \therefore x=1 \ in \ the \ equation => \ 3x+5=8$

$\rule{300}{1}$

(ii) $4x-7=13$

Let's solve your equation step-by-step.

$4x-7=13$

Step 1: Add 7 to both sides.

$4x-7+7=13+7$

$4x=20$

Step 2: Divide both sides by 4.

$\frac{4x}{4} = \frac{20}{4}$

$x=5$

Let's verify if $\bf \underline{x=5}$

$4x-7=13$

$(4\times 5) -7=13$

$20-7=13$

$13=13$

$\bf \therefore x =5\ in \ the\ equation => \ 4x-7=13$

$\rule{300}{1}$

(iii) $3(x-2)=15$

Let's solve your equation step-by-step.

$3(x-2)=15$

Step 1: Simplify both sides of the equation.

$3(x-2)=15$

(Distribute)

$(3)(x)+(3)(-2)=15$

$3x+-6=15$

$3x-6=15$

Step 2: Add 6 to both sides.

$3x-6+6=15+6$

$3x=21$

Step 3: Divide both sides by 3.

$\frac{3x}{3}=\frac{21}{3}$

$x=7$

Let's verify if $\bf \underline{x=7}$

$3(x-2)=15$

$3(7-2)=15$

$3\times 5 =15$

$15=15$

$\bf \therefore x=7 \ in \ the \ equation =>\ 3(x-2)=15$

$\rule{300}{1}$

(iv) $3(x+7)=18$

Let's solve your equation step-by-step.

$3(x+7)=18$

Step 1: Simplify both sides of the equation.

$3(x+7)=18$

(Distribute)

$(3)(x)+(3)(7)=18$

$3x+21=18$

Step 2: Subtract 21 from both sides.

$3x+21-21=18-21$

$3x=-3$

Step 3: Divide both sides by 3.

$\frac{3x}{3} =\frac{-3}{3}$

$x=-1$

Let's verify if $\bf \underline{x=-1}$

$3(x+2)=18$

$3(-1+7)=18$

$3\times 6 =18$

$18=18$

$\bf \therefore x=-1 \ in \ the \ equation =>\ 3(x+7)=18$

$\rule{300}{1}$