ALG 1 Solving Equations with Rational Coefficients

Front

What is a rational coefficient?

Back

A rational coefficient is a number that can be expressed as a fraction, where both the numerator and the denominator are integers.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the solution to the equation 4(x + 5) = 4x + 20?

Back

ALL SOLUTIONS, because both sides simplify to the same expression.

Front

How do you solve the equation 0.3(x + 1) = 0.2(x + 11)?

Back

Distribute both sides: 0.3x + 0.3 = 0.2x + 2.2. Then, isolate x to find x = 19.

Front

What is the first step in solving 2x + 3(5x - 7) = 47?

Back

Use the distributive property to expand: 2x + 15x - 21 = 47.

Front

What is the solution to the equation 3x + 2(4x - 4) = 3?

Back

x = 1, after simplifying and isolating x.

Front

What does it mean if an equation has no solution?

Back

It means there is no value for the variable that can satisfy the equation.

Front

What is the solution to the equation (x - 3) - 2 = 6 - 2(x + 1)?

Back

x = 3, after simplifying both sides.