(18) The value of x is 18.
(19) The value of x is 12.
(20) The value of x is -3.
Explanation:
(18) The equation is [tex]\frac{2}{3} x=12[/tex]
To remove the fraction, we need to multiply both sides of the equation by [tex]\frac{3}{2}[/tex].
Thus, we get,
[tex]\frac{3}{2}\times\frac{2}{3} x=12\times \frac{3}{2}[/tex]
Simplifying, we get,
[tex]x=18[/tex]
Thus, the value of x is 18.
(19) The equation is [tex]2-\frac{5}{6} x=-8[/tex]
It is given that, first subtract 2 from both sides of the equation.
[tex]2-\frac{5}{6} x-2=-8-2[/tex]
Simplifying,
[tex]-\frac{5}{6} x=-10[/tex]
Now, multiply both sides of the equation by [tex]-\frac{6}{5}[/tex], we get,
[tex]-\frac{5}{6} x\times -\frac{6}{5}=-10\times -\frac{6}{5}[/tex]
Simplifying, we have,
[tex]x=12[/tex]
Thus, the value of x is 12.
(20) The equation is [tex]-3-5x=12[/tex]
It is given that, first add 3 to both sides of the equation.
[tex]-3-5x+3=12+3[/tex]
Simplifying, we get,
[tex]-5x=15[/tex]
Now, dividing both sides by -5, we get,
[tex]-\frac{5}{-5} x=\frac{15}{-5}[/tex]
Simplifying, we get,
[tex]x=-3[/tex]
Thus, the value of x is -3.
