1. 2(6x+13)-7 >= 21
">=" is greater than or equal
2. |11x+8(x-1)+12<= 14
3. 0 <= 2x-5 < 9
4. -2< 3x +2<5
5. 3x-11>-x+17
Thanks!:)
1. 2(6x+13)-7 >= 21
">=" is greater than or equal
<= is less than or equal
2. |11x+8(x-1)| +12<= 14
3. 0 <= 2x-5 < 9
4. -2< 3x +2<5
5. 3x-11>-x+17
this is the correct given.
the first one i posted the same as this is not complete.
thanks.
1. To solve the inequality 2(6x+13)-7 >= 21:
- Start by distributing 2 to the terms inside the parentheses: 12x + 26 - 7 >= 21.
- Simplify the expression: 12x + 19 >= 21.
- Next, isolate the variable by subtracting 19 from both sides: 12x >= 2.
- Finally, divide both sides of the inequality by 12 to solve for x: x >= 2/12 or x >= 1/6.
2. To solve the inequality |11x+8(x-1)+12| <= 14:
- We can solve this by breaking it into two separate inequalities: 11x+8(x-1)+12 <= 14 and -(11x+8(x-1)+12) <= 14.
- Simplify the expressions: 11x + 8x - 8 + 12 <= 14 and -(11x + 8x - 8 + 12) <= 14.
- Combine like terms: 19x + 4 <= 14 and -19x - 4 <= 14.
- Solve each inequality separately:
- For the first inequality, subtract 4 from both sides: 19x <= 10, then divide by 19: x <= 10/19.
- For the second inequality, add 4 to both sides: -19x <= 18, then divide by -19 and flip the inequality sign since we divided by a negative number: x >= -18/19.
3. To solve the compound inequality 0 <= 2x-5 < 9:
- Treat it as two separate inequalities: 0 <= 2x-5 and 2x-5 < 9.
- Solve each inequality separately:
- For the first inequality, add 5 to both sides: 5 <= 2x, then divide by 2: 5/2 <= x.
- For the second inequality, add 5 to both sides: 2x < 14, then divide by 2: x < 7.
- Combine the solutions: 5/2 <= x < 7.
4. To solve the compound inequality -2 < 3x + 2 < 5:
- Treat it as two separate inequalities: -2 < 3x + 2 and 3x + 2 < 5.
- Solve each inequality separately:
- For the first inequality, subtract 2 from both sides: -4 < 3x, then divide by 3: -4/3 < x.
- For the second inequality, subtract 2 from both sides: 3x < 3, then divide by 3: x < 1.
- Combine the solutions: -4/3 < x < 1.
5. To solve the inequality 3x - 11 > -x + 17:
- Begin by adding x to both sides to eliminate the variable on the right side: 4x - 11 > 17.
- Then, add 11 to both sides to isolate the variable: 4x > 28.
- Finally, divide both sides by 4 to solve for x: x > 7.