solve for x: 2x + 5 < 13?

step 1: add -5
step 2: multiply by 1/2
step 3: simplify



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You treat an inequality like this exactly the same way you treat an equation: You can add the same thing to both sides, subtract the same thing from both sides, multiply both sides by the same thing, and divide both sides by the same thing. The one additional requirement is that if you multiply or divide both sides by a NEGATIVE number, then you must reverse the direction of the inedquality: > will become <, or < will become >. That rule does not apply to adding or subtracting - only to multiplying and divising.

Therefore, in this case you first subtract 5 from both sides:
2x < 8
then divide both sides by 2:
x < 4

2x + 5 < 13
2x < 13 - 5
2x < 8
x < 8/2
x < 4

2x + 5 < 13
2x < 13 - 5
2x < 8
x < 4

Therefore, x is smaller than 4.

==>2x<8,
x<4

2x + 5 <13
2x < 8
x < 4

x is smaller than 4