Quick Algebra Answers

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics (Source: Wikipedia).

In this article we are going to see some quick algebra problems with answers.

Quick Algebraic Example Problems with Answers:

Problem 1:

Given the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.

-15x - 10 - x + 3 = -16x - 20 +13

Group like terms.

-16x - 7 = -16x - 7

Add 16x + 7 to both sides and write the equation as follows

0 = 0

Hence the statement is true for all values of x and therefore all real numbers are solutions to the given equation.

Problem 2:

Given the line

5x - 5y = 7

Rewrite the eqn in slope intercept form y = mx + b and identify the value of m the slope.

-5y = -5x + 7

y = x - 7/5

The slope is given by the coefficient of x which is 1.

Problem 3:

To find the eqn of the line through the points (-1, -1) and (-1, 2), we use the slope m.

m = (y2 - y1) / (x2 - x1) = (2 - -1) / (-1 - -1) = 3 / 0

The slope is defined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since all points have equal x coordinates -1, the equation is given by:

x = -1

Problem 4:

Given the equation

2x - 4y = 10

To find the x intercept we set y = 0 and solve for x.

2x - 0 = 10

Solve for x.

x = 10 / 2

= 5

The x intercept is at the point ( 5 , 0).

Quick Algebra Practice Problems with Answers:

1. Find the statement is equal or not equal: 7(-4x - 3) - (x - 4) = -8(2x + 6) + 11

2. To find the equation of the line through the points (-2, -2) and (-2, 1), we first use the slope m.

3. Solve: 8x - 2y = 3

Answers for quick algebra:

1.Not Equal.

2.Slope m =1/0

3. The x intercept is at the point (3/8 , 0).