Solve the inequality
1. m - 7 < 6
2. x + 4.5 more than or equal to 5.5
3.p + 12 > 9
4. Translate the following statement into an inequality: Five less than a number is at least nine.
x - 5 more than or equal to 9
"≥" can be obtained by using ">" key with "option" key.
An inequality is treated just like an equation, except that multiplying/dividing by a negative value reverses the carat (< to >).
To solve inequalities, we follow similar rules as solving equations, but with a few differences. Let's solve the given inequalities step by step:
1. m - 7 < 6:
To solve this inequality, we want to isolate the variable m on one side of the inequality sign.
First, let's add 7 to both sides of the inequality to get rid of the -7:
m - 7 + 7 < 6 + 7
m < 13
So, the solution to the inequality is m < 13.
2. x + 4.5 ≥ 5.5:
Similarly, let's isolate the variable x on one side of the inequality.
First, subtract 4.5 from both sides of the inequality:
x + 4.5 - 4.5 ≥ 5.5 - 4.5
x ≥ 1
So, the solution to the inequality is x ≥ 1.
3. p + 12 > 9:
Again, let's isolate the variable p.
First, subtract 12 from both sides of the inequality:
p + 12 - 12 > 9 - 12
p > -3
So, the solution to the inequality is p > -3.
4. The inequality for the given statement, "Five less than a number is at least nine," can be translated as:
x - 5 ≥ 9
To solve it, isolate the variable x by adding 5 to both sides of the inequality:
x - 5 + 5 ≥ 9 + 5
x ≥ 14
So, the solution to the inequality is x ≥ 14.
Remember, when solving inequalities, if you multiply or divide both sides by a negative number, the inequality sign flips.