Solve the inequality and sketch the solution:
-3≤ 2(x+4)< 14
-3 ¡Ü 2(x+4)< 14
Divide each term in the inequality by 2
-3/2 ¡Ü x+4 < 7
Subtract 4 from all terms.
-11/2 ¡Ü x < 3
You do the sketching
Got it! Thanks.
To solve the given inequality, we need to isolate the variable x.
Let's first solve the left side of the inequality -3 ≤ 2(x+4).
-3 ≤ 2(x+4)
Divide both sides of the inequality by 2:
(-3)/2 ≤ (2(x+4))/2
-3/2 ≤ x + 4
Subtract 4 from both sides of the inequality:
-3/2 - 4 ≤ x + 4 - 4
-11/2 ≤ x
Now, let's solve the right side of the inequality 2(x+4) < 14.
2(x+4) < 14
Divide both sides of the inequality by 2:
(2(x+4))/2 < 14/2
x + 4 < 7
Subtract 4 from both sides of the inequality:
x + 4 - 4 < 7 - 4
x < 3
Therefore, the solution to the inequality -3 ≤ 2(x+4) < 14 is:
-11/2 ≤ x < 3.
To sketch the solution on a number line, mark an open circle at -11/2 (since it is not included in the solution) and a closed circle at 3 (since it is included in the solution). Then, draw a line between the two points and shade it to the left of -11/2 and to the right of 3.