Algebra 1 Homework Help for Kids and Teens

Algebra Homework Help

Expressions, Equations and Inequalities

An expression represents an operation or set of operations, like (5 + 7) ÷ 4 or 4^3. Expressions may contain both numbers and variables. Equations state that the results of two expressions are equal, like 2(x + 3) = 2x + 6. When you solve equations by isolating the variable, you'll assume that both sides are equal. If there is no variable that can make the equation true, it's considered to have no solution.

Inequalities state that the result of one expression is greater than or less than the result of another. For example, 6x > 2x states that 6x is greater than 2x. If the inequality sign were underlined, this would indicate that 6x was greater than or equal to 2x.

Problem Solving and Graphing

In algebra, you'll use equations and inequalities to solve problems, and you'll represent those solutions graphically. For example, you might be given a problem like this one:

'Sam pays a tax rate of 20%, but he also gets a tax credit of $6,000. What is Sam's after-tax income if his gross income is $40,000? Graph an equation representing this problem.'

First, you'd represent this problem with an equation like this one: x - 0.20x + 6,000 = y. The variable 'x' is Sam's gross income and 'y' represents his after-tax income. Since the question is asking about Sam's after-tax income when his gross income is $40,000, you can answer the question by plugging 40,000 in for 'x' and solving for 'y':

(40,000) - (40,000)(0.20) + 6,000 = y

y = 38,000

To answer the second part of the question, which asks you to graph the equation, you can employ one of two techniques. You can use the 'plug and chug' method, which means you plug in a few values for 'x' and solve for 'y.' This will generate a table of coordinate points. By plotting these points and drawing a line through them, you can identify the line representing the equation.

You can also manipulate the equation so that it's in slope-intercept form: y = mx + b. For equations in this form, 'm' is the slope of the line and 'b' is the line's y-intercept (the point where it crosses the y-axis). To put x - 0.20x + 6,000 = y in this form, simplify it to y = 0.80x + 6,000. The slope of 0.80 tells you that the line increases by 0.80 of a unit for every unit increase in the value of 'x,' and the y-intercept of 6,000 tells you where the line intersects with the y-axis.