Solve using the addition and multiplication principles. 8-8y-5y < 47
-13y < 39
-y < 3
y > -3
To solve the inequality 8 - 8y - 5y < 47 using the addition and multiplication principles, we'll simplify the equation step by step.
Step 1: Combine like terms on the left side of the inequality.
Starting with 8 - 8y - 5y, we can combine the y terms:
8 - 8y - 5y = 8 - (8y + 5y) = 8 - 13y.
Step 2: Rewrite the inequality with the simplified expression:
8 - 13y < 47.
Step 3: Isolate the variable term by subtracting 8 from both sides of the inequality:
8 - 13y - 8 < 47 - 8,
-13y < 39.
Step 4: Divide both sides of the inequality by -13. Remember, when dividing an inequality by a negative number, the direction of the inequality symbol will be flipped.
(-13y) / -13 > 39 / -13,
y > -3.
Therefore, the solution to the inequality 8 - 8y - 5y < 47 is y > -3.