How do you solve # -5(x-7)<15#?

1 Answer
Tony B
Dec 27, 2016

#x>4#

Explanation:

Multiply everything inside the brackets by -5 giving:

#-5x+35<15#

Subtract 35 from both sides

#-5x+0<15-35#

#-5x< -20#
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Short cut approach: when something changes sides with the = its sign becomes opposite ( for add, subtract, divide or multiply)

So if we had #-5x=-20# then this becomes: #+20=+5x#

It is the same thing for inequalities.
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#-5x<-20" "vec("swapping sides")" " +20<+5x#

Same thing but with a different method:

Multiply both sides by (-1) and turn the inequality round the other way:
#" "-5x" "<" "-20#

#" "(-1)xx(-5x)" ">" "(-1)xx(-20)#

#" "5x" ">" "20#

Divide both sides by 5

#" "x" ">" "4#

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