Boost Your Pre-Algebra Skills with Examples and Solutions

High School
Algebra
Pre-Algebra

Solve each of the following equations for x. Determine the exact value for x and a decimal approximation correct to four decimals places.
1. $8 x - 15 = 0$ (Solving this equation will locate the x-intercept on the gtaph of $y = 8^{x} - 15$ )
2. $\log (x + 6) = \log (3 x - 2) + 2$ (Solving this equation will determine the x-coordinate of the point of intersection of the functions $y = \log (x + 6)$ and $y = \log (3 x - 2) + 2 .)$
3. $4400 = 2000 {(1 + \frac{0.045}{12})}^{12 x}$ (Solving this equation will determine the amount of time it takes an investment $2000 to grow to $4400 if interest is $4.5 %$ compounded monthly.)

kuCAu 2021-09-16

Evaluate the expression
$\frac{1}{2} \cdot \frac{2}{3} \div \frac{3}{2} - \frac{1}{12} \cdot (- \frac{1}{3})$
A. $\frac{1}{2} \cdot \frac{2}{3} \div \frac{3}{2} - \frac{1}{12} \cdot (- \frac{1}{3}) = ?$
B. The answeris undefined.

Chaya Galloway 2021-09-16

Solve: $\frac{x + 3}{4} = \frac{x - 2}{3} + \frac{1}{4}$ .

sodni3 2021-09-16

I need help with fractions, out of 101 roses, 57 are red, what fraction is not in red color.

Dillard 2021-09-16

Tell whether the ratios form a proportion.
$\frac{9}{2}, \frac{2}{3}$
a) Yes
b) No

aortiH 2021-09-16

A. Characterized the x-intercept and the y-intercept of the given linear equations below. Then use them to draw and characterized the graph of the linear equation.
Note: characterized means to tell whether the slope of the line is positive or negative and to tell whether the line is pointing upward to the right or downward to the right.
1. $- 6 x + 3 y = - 18$
2. $3 x + 2 y = 9 x + 12$

ossidianaZ 2021-09-16

The solution set of the equation ${(2 y - 3)}^{\frac{1}{3}} - {(4 y + 5)}^{\frac{1}{3}} = 0$

abondantQ 2021-09-16

Find the average rate of change of the function $f (x) = 5 x$ from $x_{1} = 0$ to $x_{2} = 3$ .
The average rate of change is _______. (Simplify your answer.)

fortdefruitI 2021-09-15

The function $2 (4 x + 1)$ and $8 x + 2$ are either equivalent inequalities, equivalent equation, equivalent expression, or not equivalent.

Ramsey 2021-09-15

Simplify a Complex Rational Expression by Writing It as Division. In the following exercises, simplify
$\frac{x - \frac{3 x}{x + 5}}{\frac{1}{x + 5} + \frac{1}{x - 5}}$

Brittney Lord 2021-09-15

Grayson deposited $4,500 into a new account.
- The account earned annual simple interest.
- No withdrawals or deposits were made.
- At the end of 2 years, the balance of the account was $5,265.
What is the annual interest rate on this account?
$I = P r t$ , plug in numbers and solve equation in your calculator.
Convert ALL answer choices to decimals (percent divided by 100)
A. $4.7 %$
B. $5.2 %$
C. $7.3 %$
D. $8.5 %$

Tobias Ali 2021-09-15

Find any holes, vertical asymptotes, and horizontal asymptotes for the following rational function.
$f (x) = \frac{2 (x - 3) (3 x + 5)}{3 (3 x + 4) (x - 3)}$
The hole(s) is _
The Vertical Asymptote(s) is _
The Horizontal Asymptote is _____

Ernstfalld 2021-09-15

How to simplify this without using fractions in the power? We didn't learn to rationalize with fractions in our school.
$(x \sqrt{x})^{3} \cdot 3 \sqrt{x \sqrt[3]{x}} = x^{4} \sqrt[6]{x^{5}}$

Brittney Lord 2021-09-15

$\frac{5}{4} x + 3 = \frac{1}{4} + \frac{1}{4} x$

Reggie 2021-09-15

Simplify the following expression:
$(2 - 3 y) + (6 + 8 y)$

Burhan Hopper 2021-09-15

Solve the equation. Express numbers as integers or simplified fractions.
$2 - 4 (4 z - 1) = - 1$

Suman Cole 2021-09-15

Perform the addition or subtraction and simplify.
$\frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}}$

banganX 2021-09-15

Solve the equation $2 + \frac{5}{x - 4} = \frac{x + 1}{x - 4}$

emancipezN 2021-09-15

A bag contains three red balls numbered 1, 2, 3 and six white balls numbered 4, 5, 6, 7, 8, 9. A ball is drawn. What is the probability that the ball is the following? (Enter your probabilities as fractions.)
(a) red and even-numbered
(b) red or even-numbered
(c) white or odd-numbered

Falak Kinney 2021-09-15

Express $\frac{1}{11}$ as a repeating decimal, using a slash to indicate the repeating digits. What are the decimal expansions of the following fractions: $\frac{2}{11}, \frac{3}{11}, \frac{9}{11} and \frac{11}{11}$ ?

Getting your pre Algebra solved becomes much easier when you have all the answers to your questions by taking a closer look at the various examples dealing with Pre-Algebra subjects. We have intentionally collected the list of pre-algebra equations and various solving equations with decimals problems to help you see various examples that explain how certain solutions are found. Still, if something sounds unclear or you are concerned about some solution that has been provided, approach pre-algebra with reverse engineering approach (going backwards).

Pre-Algebra

Improve Your Algebra Skills with Practice Problems