Question

Solve the following equations and check your answers.
i) $5x-2=18$
ii) $\frac{1}{4}y+\frac{1}{2}=5$
iii) $3x+\frac{1}{5}=2-x$
iv) $8x+5=6x-5$

Answer 1

$\left(i\right)5x-2=18$

$\Rightarrow 5x=20$

$\Rightarrow k=4$

check:

$LHS\Rightarrow 5\left(4\right)-2=18=RHS$

$\therefore x=4$

$\left(ii\right)\frac{1}{4}y+\frac{1}{2}=5$

$y+2=20$

$\Rightarrow y=18$

Check:

$LHS\Rightarrow \frac{1}{4}\left(18\right)+\frac{1}{2}\Rightarrow \frac{18+2}{4}$

$\Rightarrow 5=RHS$

$\therefore y=18$

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

$4x=2-\frac{1}{5}$

$4x=\frac{9}{5}$

$x=\frac{9}{20}$

check:

$LHS\Rightarrow 3x+\frac{1}{5}=3\left(\frac{9}{20}\right)+\frac{1}{5}$

$\Rightarrow \frac{31}{20}\Rightarrow 2-\frac{9}{20}=RHS$

$\Rightarrow x=\frac{9}{20}$

$\left(iv\right)8x+5=6x-5$

$2x=-10$

$x=-5$

check:

$LHS\Rightarrow 8x+5\Rightarrow 8(-5)+5$

$\Rightarrow -35\Rightarrow 6(-5)-5$

$\Rightarrow RHS$

$\Rightarrow x=-5$