solve for x: -5 is less than or equal to 2(2x+5)-7<12
thanks :)
-5 < 2(2x+5)-7 <12
-5 ≤ 4x+3 < 12
subtract 3
-8 ≤ 4x < 9
divide by 4
-2 ≤ x < 2.25
2(2x+5)-7<12
2(2(-5)+5)-7<12
2(-10+5)-7<12
2(-5)-7<12
-10-7<12
-17<12
neither of those solve for x...how do i continue from -2 is less than or equal to x<(9/4)?
-2 ≤ x < 2.25 is the solution
It means that x can be any number between -2 and +2.25
including the -2, but excluding the +2.25
On a number line, mark -2 and 2.25
place a solid circle on the -2, meaning that value is included
place an open circle on the 2.25, meaning we can't have the actual 2.25
join the two circles with a solid line, showing you want all possible values in between.
To be able to answer your question, you must have studied the method I just described.
oh ok. thanks.
To solve for x in the inequality -5 ≤ 2(2x+5) - 7 < 12, you need to isolate x.
First, let's simplify the expression:
-5 ≤ 2(2x+5) - 7 < 12
Start by distributing 2 to the terms inside the parentheses:
-5 ≤ 4x + 10 - 7 < 12
Combine like terms:
-5 ≤ 4x + 3 < 12
Next, we want to isolate the variable x. To do that, we need to get rid of the 3 on each side. Subtract 3 from all parts of the inequality:
-5 - 3 ≤ 4x + 3 - 3 < 12 - 3
Simplify:
-8 ≤ 4x < 9
Now, to isolate x, divide all parts of the inequality by 4:
-8/4 ≤ 4x/4 < 9/4
Simplify:
-2 ≤ x < 9/4
So the solution for x is -2 ≤ x < 9/4.