I need help in solving two-step inequalities.
7 - 4w <_ 19
7 - 4w <= 19
-4w <= 19 - 7
-4w <= 12 Divide both sides with -4
( Remark: When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol. )
w >= -3
To solve the two-step inequality 7 - 4w ≤ 19, you need to isolate the variable "w". Here's how you can do it:
Step 1: Start by subtracting 7 from both sides of the inequality:
7 - 7 - 4w ≤ 19 - 7
This simplifies to:
-4w ≤ 12
Step 2: Divide both sides of the inequality by -4. Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the direction of the inequality sign:
-4w / -4 ≥ 12 / -4
This simplifies to:
w ≥ -3
So the solution to the inequality 7 - 4w ≤ 19 is w ≥ -3.
To solve a two-step inequality, you need to isolate the variable on one side of the inequality symbol, just like you would in solving an equation. Here's how you can solve the given inequality:
Step 1: Start by subtracting 7 from both sides of the inequality to move the constant term to the other side:
7 - 7 - 4w <= 19 - 7
Simplifying this gives you:
-4w <= 12
Step 2: Divide both sides of the inequality by -4. Since you are dividing by a negative number, the direction of the inequality symbol flips:
-4w / -4 >= 12 / -4
Simplifying this gives you:
w >= -3
So, the solution to the inequality 7 - 4w <= 19 is w >= -3.
You can check your solution by plugging in a number greater than or equal to -3 into the original inequality and seeing if the inequality holds.