WCA1R One Step Equations Multiplication worksheet - Free Printable

Here are the solutions for the one-step equations. To solve these, we need to isolate $x$ by doing the opposite operation (inverse operation) on both sides of the equation.

Step-by-Step Solutions:

(1) $2x = 12$
Divide both sides by 2:
$x = \frac{12}{2}$
$x = 6$

(2) $3x = -15$
Divide both sides by 3:
$x = \frac{-15}{3}$
$x = -5$

(3) $-5x = 25$
Divide both sides by -5:
$x = \frac{25}{-5}$
$x = -5$

(4) $-6x = -24$
Divide both sides by -6:
$x = \frac{-24}{-6}$
(Negative divided by negative is positive)
$x = 4$

(5) $42 = -7x$
Divide both sides by -7:
$x = \frac{42}{-7}$
$x = -6$

(6) $8x = -14$
Divide both sides by 8:
$x = \frac{-14}{8}$
Simplify the fraction by dividing top and bottom by 2:
$x = -\frac{7}{4}$ (or $-1.75$)

(7) $-33 = -6x$
Divide both sides by -6:
$x = \frac{-33}{-6}$
Simplify the fraction by dividing top and bottom by 3:
$x = \frac{11}{2}$ (or $5.5$)

(8) $\frac{5}{6}x = 10$
Multiply both sides by the reciprocal ($\frac{6}{5}$):
$x = 10 \cdot \frac{6}{5}$
$x = \frac{60}{5}$
$x = 12$

(9) $\frac{2}{5}x = -20$
Multiply both sides by the reciprocal ($\frac{5}{2}$):
$x = -20 \cdot \frac{5}{2}$
$x = \frac{-100}{2}$
$x = -50$

(10) $-6 = -\frac{1}{3}x$
Multiply both sides by the reciprocal ($-3$):
$x = -6 \cdot (-3)$
$x = 18$

(11) $\frac{5}{11}x = \frac{15}{22}$
Multiply both sides by the reciprocal ($\frac{11}{5}$):
$x = \frac{15}{22} \cdot \frac{11}{5}$
Cross-cancel: 15 and 5 become 3 and 1; 11 and 22 become 1 and 2.
$x = \frac{3 \cdot 1}{2 \cdot 1}$
$x = \frac{3}{2}$ (or $1.5$)

(12) $\frac{3}{7}x = \frac{9}{14}$
Multiply both sides by the reciprocal ($\frac{7}{3}$):
$x = \frac{9}{14} \cdot \frac{7}{3}$
Cross-cancel: 9 and 3 become 3 and 1; 7 and 14 become 1 and 2.
$x = \frac{3 \cdot 1}{2 \cdot 1}$
$x = \frac{3}{2}$ (or $1.5$)

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Final Answer:
(1) $x = 6$
(2) $x = -5$
(3) $x = -5$
(4) $x = 4$
(5) $x = -6$
(6) $x = -\frac{7}{4}$ (or $-1.75$)
(7) $x = \frac{11}{2}$ (or $5.5$)
(8) $x = 12$
(9) $x = -50$
(10) $x = 18$
(11) $x = \frac{3}{2}$ (or $1.5$)
(12) $x = \frac{3}{2}$ (or $1.5$)