Solving Equations and Inequalities

Front

What is the first step in solving the inequality 5(6 + 3r) + 7 ≥ 127?

Back

Distribute the 5 to both terms inside the parentheses.

Front

How do you isolate the variable in the equation 3x + 15 = 3(x + 5)?

Back

Subtract 15 from both sides and simplify.

Front

What is the mistake in the equation 19 - 2k = 3k - 1 when adding 3k?

Back

The mistake is that instead of adding 3k, you should subtract 3k.

Front

What is the solution to the equation 5x + 34 = -2(-7x + 1)?

Back

x = 4.

Front

How do you solve the equation 2(2x + 3) = -6(x + 9)?

Back

Distribute both sides, combine like terms, and isolate x.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that the equation is true for all values of the variable.

Front

What is the process of checking your solution in an equation?

Back

Substitute the solution back into the original equation to verify.

Front

What is the significance of the equality sign in equations?

Back

It indicates that the expressions on both sides are equal.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

How do you handle inequalities when multiplying or dividing by a negative number?

Back

You must reverse the inequality sign.