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Algebra 1 : How to solve one-step equations

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Example Questions

Example Question #11 : How To Solve One Step Equations

What is the smaller root of $\displaystyle (x+5)(x-2)=0$?

Possible Answers:

$\displaystyle -5$

$\displaystyle 5$

$\displaystyle 0$

$\displaystyle 2$

$\displaystyle -2$

Correct answer:

$\displaystyle -5$

Explanation:

To determine the roots of the equation, you must set each expression equal to 0. In this case, there are two expressions being multiplied. Thus, you must set x+5=0 $\displaystyle x+5=0$ and x-2=0 $\displaystyle x-2=0$, which would give you $\displaystyle -5$ and $\displaystyle 2$ as roots, with $\displaystyle -5$ being the smaller root.

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Example Question #12 : How To Solve One Step Equations

Solve for $\displaystyle x$:

$\displaystyle 5x-3+2x=9x+1$

Possible Answers:

$\displaystyle 2$

$\displaystyle 1$

$\displaystyle 0$

$\displaystyle -2$

$\displaystyle -1$

Correct answer:

$\displaystyle -2$

Explanation:

Simplify the equation to get $\displaystyle 7x-3=9x+1$. Simplify further to get 2x=-4 $\displaystyle 2x=-4$, which then gives you x=-2 $\displaystyle x=-2$.

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Example Question #13 : How To Solve One Step Equations

$Solve\; for\; w\; in \;the \;equation,\; -4w = 12$ $\displaystyle Solve\; for\; w\; in \;the \;equation,\; -4w = 12$

Possible Answers:

$\displaystyle -5$

$\displaystyle -3$

$\displaystyle 3$

$\displaystyle 8$

Correct answer:

$\displaystyle -3$

Explanation:

\(\displaystyle -4 w = 12\)
\(\displaystyle \fn_cm Divide \; both\;sides\;of\;-4 w = 12\;by\;-4\)\(\displaystyle w = 12\div (-4)\)
\(\displaystyle =\frac{4\times 3}{-4}=\frac{3}{-1}=-3\)\(\displaystyle w = -3\)

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Example Question #14 : How To Solve One Step Equations

$Solve\; for\; p\; in\; -\frac{p}{7} = \frac{7}{2}$ $\displaystyle Solve\; for\; p\; in\; -\frac{p}{7} = \frac{7}{2}$

Possible Answers:

$\frac{-7}{2}$ $\displaystyle \frac{-7}{2}$

$\displaystyle -14$

$\frac{-49}{2}$ $\displaystyle \frac{-49}{2}$

$\displaystyle 2$

Correct answer:

$\frac{-49}{2}$ $\displaystyle \frac{-49}{2}$

Explanation:

 \(\displaystyle Multiply\; both\; sides\; of\; -\frac{p}{7} = \frac{7}{2}\; by \; -7\)\(\displaystyle \fn_cm \fn_cm \frac{-7p}{-7} = \frac{-7\times7 }{2}\)
\(\displaystyle \fn_cm p=\frac{-49}{2}\)

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Example Question #15 : How To Solve One Step Equations

Solve for $\displaystyle x$.

$\displaystyle 5x - 2(1+2x) = 10 - (x-1)$

Possible Answers:

$x = \frac{13}{10}$ $\displaystyle x = \frac{13}{10}$

$x = \frac{13}{2}$ $\displaystyle x = \frac{13}{2}$

x = 13 $\displaystyle x = 13$

$x = \frac{11}{2}$ $\displaystyle x = \frac{11}{2}$

$x = \frac{11}{10}$ $\displaystyle x = \frac{11}{10}$

Correct answer:

$x = \frac{13}{2}$ $\displaystyle x = \frac{13}{2}$

Explanation:

$\displaystyle 5x - 2(1+2x) = 10 - (x-1)$

Multiply the terms in parentheses using the distributive property.

$\displaystyle 5x - 2 - 4x = 10 - x + 1$

Then, combine like terms on both sides of the equation.

$\displaystyle x -2 = 11 - x$

Then, put the $\displaystyle x$ terms on the left and the integers on the right:

2x = 13 $\displaystyle 2x = 13$

Divide both sides by two to isolate $\displaystyle x$.

$x = \frac{13}{2}$ $\displaystyle x = \frac{13}{2}$

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Example Question #16 : How To Solve One Step Equations

Solve for $\small x$ $\displaystyle \small x$.

x-8=-1 $\displaystyle x-8=-1$

Possible Answers:

x=7 $\displaystyle x=7$

x=3 $\displaystyle x=3$

x=-2 $\displaystyle x=-2$

x=-9 $\displaystyle x=-9$

x=13 $\displaystyle x=13$

Correct answer:

x=7 $\displaystyle x=7$

Explanation:

x-8=-1 $\displaystyle x-8=-1$

Add 8 to both sides.

$\displaystyle x-8+8=-1+8$

Simplify.

x=7 $\displaystyle x=7$

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Example Question #17 : How To Solve One Step Equations

Solve for $\displaystyle x$:

$\displaystyle 25x-10-5x=40-5x$

Possible Answers:

$\displaystyle 1$

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle 5$

$\displaystyle 4$

Correct answer:

$\displaystyle 2$

Explanation:

Since both sides of the equation have -5x $\displaystyle -5x$, you can eliminate both from the equation with the knowledge that they would cancel each other out. This gives you the shorter equation of

$\displaystyle 25x-10=40$.

Add $\displaystyle 10$ to both sides to get

25x=50 $\displaystyle 25x=50$.

Finally, divide both sides by $\displaystyle 25$ to get x=2 $\displaystyle x=2$.

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Example Question #18 : How To Solve One Step Equations

Solve for $\displaystyle w$

$\frac{w}{11}=11$ $\displaystyle \frac{w}{11}=11$

Possible Answers:

$\displaystyle 1$

$\displaystyle 11$

121 $\displaystyle 121$

$\displaystyle 0$

None of the other answers

Correct answer:

121 $\displaystyle 121$

Explanation:

Solve by isolating $\displaystyle w$ on one side of the equation by itself

Multiply each side of equation by 11

w=121 $\displaystyle w=121$

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Example Question #19 : How To Solve One Step Equations

Solve for $\displaystyle p$.

$\displaystyle -15 + p=6$

Possible Answers:

$\displaystyle -9$

$-\frac{2}{5}$ $\displaystyle -\frac{2}{5}$

$\displaystyle 21$

$\displaystyle -21$

$\displaystyle 0$

Correct answer:

$\displaystyle 21$

Explanation:

-15+p=6 $\displaystyle -15+p=6$

Add 15 to each side of the equation.

p=21 $\displaystyle p=21$

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Example Question #20 : How To Solve One Step Equations

Solve for $\displaystyle x$:

$\frac{3}{5}x = 6$ $\displaystyle \frac{3}{5}x = 6$

Possible Answers:

$\displaystyle 30$

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\frac{18}{5}$ $\displaystyle \frac{18}{5}$

$\displaystyle 10$

Correct answer:

$\displaystyle 10$

Explanation:

Multiply both sides of the equation by the reciprocal of $\frac{3}{5}$ $\displaystyle \frac{3}{5}$, which is $\frac{5}{3}$ $\displaystyle \frac{5}{3}$. This will give us:

$x=6*\frac{5}{3}$ $\displaystyle x=6*\frac{5}{3}$

We can think of this as dividing by 3 and multiplying by 5. It doesn't matter what order we do those opperations in, so we'll divide by 3 first. $6 \div 3 =2$ $\displaystyle 6 \div 3 =2$.

Now we'll multiply by 5: 2*5=10 $\displaystyle 2*5=10$.

So our answer is 10.

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Algebra 1 : How to solve one-step equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : How To Solve One Step Equations

Example Question #12 : How To Solve One Step Equations

Example Question #13 : How To Solve One Step Equations

Example Question #14 : How To Solve One Step Equations

Example Question #15 : How To Solve One Step Equations

Example Question #16 : How To Solve One Step Equations

Example Question #17 : How To Solve One Step Equations

Example Question #18 : How To Solve One Step Equations

Example Question #19 : How To Solve One Step Equations

Example Question #20 : How To Solve One Step Equations

All Algebra 1 Resources

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