The direction of the inequality remains unchanged. The direction changes when you divide or multiply both sides by a negative number. It also changes if both sides are raised to a negative exponent.
-5x + 4 > -2x + 31 add 2x and subtract 4 to both sides; -3x > 27 divide by -3 to both sides and change the symbol of the inequality; x < 9
You solve an inequality the same way you solve an equality. You add and subtract, multiply and divide, both sides by the same value in order to isolate one of the variables. The only extra thing you need to remember is that if you multiply or divide by a negative number, you must reverse the order of the inequality, i.e. less than or equal becomes greater than or equal.
I am assuming that the original equation is 33z-4-20=z-5. Subtract z from both sides. Add 4 to both sides, as well as add 20 to both sides. Divide both sides by 32.
2t-6=3-t 3t-6=3 Add t to both sides 3t=9 Add 6 to both sides t=3 Divide both sides by 3
The direction of the inequality remains unchanged. The direction changes when you divide or multiply both sides by a negative number. It also changes if both sides are raised to a negative exponent.
Just add 25 to both sides of the inequality - that way, you will isolate the "x", i.e., solve for "x".
You would add 9 to both sides, canceling out the 9 on the left. Now you have 7n
Add 25 to both sides to give x ≤ 58
3a-2 > 5a-9 Subtract 5a from both sides: -2a-2 > -9 Add 2 to both sides: -2a > -7 Divide both sides by -2 and reverse the inequality sign: Solution: a < 3.5 on the number line
You can add, subtract, multiply, or divide both sides of the equation or inequality by the same number. Don't multiply or divide by zero. In the case of an inequality, if you multiply or divide by a negative number, the sign of the inequality must be reversed. E.g., if you multiply both sides by -2, a "less-than" sign should be replaced by a "greater-than" sign.
5n - 1 ≥ 6 Add 1 to both sides: 5n ≥ 7 Divide both sides by 5: n ≥ 7/5 = 1.4
8n - 2 > 17n + 9 subtract 17n and add 2 to both sides -9n > 11 divide by -9 to both sides and change the symbol of the inequality n < -11/9
-5x + 4 > -2x + 31 add 2x and subtract 4 to both sides; -3x > 27 divide by -3 to both sides and change the symbol of the inequality; x < 9
In simple cases such as these, you can solve inequalities just like an equation. In this case, you add 3 to both sides.
You solve an inequality the same way you solve an equality. You add and subtract, multiply and divide, both sides by the same value in order to isolate one of the variables. The only extra thing you need to remember is that if you multiply or divide by a negative number, you must reverse the order of the inequality, i.e. less than or equal becomes greater than or equal.
X - 1 <= 2 just treat like equation and add 1 to both sides x <= 3