Solve x/2 + x/5 = 7
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 10 |
Step-by-step solution
6 steps-
1 Given\frac{x}{2} + \frac{x}{5} = 7
Solve for x.
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2 Combine like terms\frac{7 x}{10} = 7
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3 Multiply both sides by 10 to clear the fractions
10 is the least common multiple of the denominators. Multiplying every term on both sides by it cancels each fraction, so the rest of the work uses whole numbers. The equation stays balanced because both sides were multiplied by the same number.
7 x = 70 -
4 Divide both sides by 7
Dividing both sides by 7 undoes the multiplication by 7, so the variable is left on its own. Both sides change in the same way, so the equation stays true (dividing by 0 is the one thing that is never allowed).
x = \frac{70}{7} -
5 Simplifyx = 10
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6 Check\begin{aligned}x = 10:\quad 7 = 7\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 10 | 7 | 7 | ✓ |
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