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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #151 : Equations / Inequalities

The sum of four consecutive integers equal 98. What is the sum of the smallest and the largest number in the set?

Possible Answers:

Correct answer:

Explanation:

Let a variable represent the smallest number in the set. Every consecutive number after the first number will be one unit greater than the other. Then, the four numbers that sum up to 98 are:

(x)+(x+1)+(x+2)+(x+3)=98

where every term in parenthesis represents a number. Add and solve for .

4x+6=98

x=23

The smallest number is , and the largest number is x+3 . Therefore:

x+(x+3)= 23+(23+3)=23+26=49

The correct answer is:

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Example Question #25 : How To Find The Solution To An Equation

Solve for .

3a+4-4(a+2)=-12a+6(a-2)

Possible Answers:

5/8

8/5

-8/5

-5/8

Correct answer:

-8/5

Explanation:

The question asks for the value of .

To isolate , use the distributive properties to remove the parentheses then combine like terms.

3a+4-4(a+2)=-12a+6(a-2)

3a+4-4a-8=-12a+6a-12

-a-4=-6a-12

Finally isolate by balancing the equation.

5a=-8

a=-8/5

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Example Question #26 : How To Find The Solution To An Equation

Find the solution to this equation: $10x+25(x-\frac{1}{25})=174$

Possible Answers:

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

x=5

x=-5

None of the other answers.

$x=\frac{1}{5}$

Correct answer:

x=5

Explanation:

To find the solution to this equation you must completely isolate x.

$10x+25(x-\frac{1}{25})=174$

Start by dealing with the parenthesis first. Distribute the 25:

10x+25x-1=174

Combine the x terms and move the constant over:

35x=175

Finally divide the constant away from x to solve:

x=5

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Example Question #3 : Solving Equations And Inequallities

Solve for x: 12x-5(x-2)=45

Possible Answers:

x=5

x=7

$x=\frac{7}{55}$

$x=\frac{55}{7}$

x=8

Correct answer:

x=5

Explanation:

12x-5(x-2)=45

Simplify the parenthesis:

12x-5x+10=45

Combine the terms with x's:

7x+10=45

Combine constants:

$7x=35\rightarrow \mathbf{x=5}$

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Example Question #152 : Equations / Inequalities

Solve for x: $2x=\frac{3}{2}-5$

Possible Answers:

$x=\frac{7}{4}$

$x=-\frac{7}{4}$

None of these

$x=\frac{4}{3}$

$x=-\frac{4}{7}$

Correct answer:

$x=-\frac{7}{4}$

Explanation:

$2x=\frac{3}{2}-5$

Simplify the right side:

$2x=\frac{3}{2}-\frac{10}{2}$

$2x=-\frac{7}{2}$

Isolate x:

$\frac{1}{2}*2x=-\frac{7}{2}*\frac{1}{2}$

$\mathbf{x=-\frac{7}{4}}$

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Example Question #153 : Equations / Inequalities

Solve for

1=5+x

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

1 = 5 + x

1-5 = 5+x-5

-4=x

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Example Question #2 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

6x-9-x=2x-6

Possible Answers:

Correct answer:

Explanation:

First. combine like terms to get

5x-9=2x-6 .

Then, add and subtract from both sides to separate the terms.

This gives you 3x=3 .

Finally, divide both sides by to get a solution of x=1 .

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Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

8(x+5)=16

Possible Answers:

None of the other answers

$\frac{11}{8}$

$-\frac{11}{8}$

Correct answer:

Explanation:

First, you must multiply the left side of the equation using the distributive property.

This gives you 8x+40=16 .

Next, subtract from both sides to get 8x=-24 .

Then, divide both sides by to get x=-3 .

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Example Question #154 : Equations / Inequalities

$A\ \blacksquare\ B= \frac{A + B}{2}-\frac{2}{A-B}$

If $8\ \blacksquare\ B = 6$ , find the value of .

Possible Answers:

Correct answer:

Explanation:

The simplest way to solve this is to test the answer choices provided by plugging them in the equation. Start with the number in the middle, which in this case is 6. Replace every "B" in the equation with "6", and solve.

$\frac{8+(6)}{2}-\frac{2}{8-(6)}=\frac{14}{2}-\frac{2}{2}=7-1=6$

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Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Simplify the following:

$\frac{2x}{x+3} + \frac{4}{x}$

Possible Answers:

$\frac{2x^2+4x+12}{x(x+3)}$

$\frac{2x+4}{2x+3}$

$\frac{8x}{x^2+3x}$

$\frac{2x+4}{x(x+3)}$

Correct answer:

$\frac{2x^2+4x+12}{x(x+3)}$

Explanation:

Before you can add the two numerators from the fractions, the fractions must have a common denominator. The common denominator will be the Lowest Common Denominator (LCD). When you are dealing with variables, you get this by multiplying the two denominators together:

$\frac{2x}{x+3} + \frac{4}{x} = \frac{?}{x(x+3)}$

To follow through with this LCD, you must multiply each fraction by the other fraction's denominator so that they end up with common denominators. The first fraction needs to be multiplied by $\frac{x}{x}$ and the second fraction needs to be multiplied by $\frac{x+3}{x+3}$ . Note that both of these are equivalent to ONE, so the value of the fraction does not change:

$\frac{(2x)(x)}{(x+3)(x)} + \frac{(4)(x+3)}{(x)(x+3)} = \frac{2x^2}{x(x+3)} + \frac{4x+12}{x(x+3)}$

Now that the two fractions have common denominators, you can add the two numerators:

$\frac{2x^2+4x+12}{x(x+3)}$

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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #151 : Equations / Inequalities

Example Question #25 : How To Find The Solution To An Equation

Example Question #26 : How To Find The Solution To An Equation

Example Question #3 : Solving Equations And Inequallities

Example Question #152 : Equations / Inequalities

Example Question #153 : Equations / Inequalities

Example Question #2 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #154 : Equations / Inequalities

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

All Algebra 1 Resources

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