How do you solve #7(t^2+5t-9)+t=t(7t-2)+13#?

Answer 1

Nathan Axel

#t=2#

#"the first step is to distribute the brackets on both sides"#

#rArr7t^2+35t-63+t=7t^2-2t+13#

#7t^2+36t-63=7t^2-2t+13larr" simplify left side"#

#"collect variables on left and numeric values on right"#

#cancel(7t^2)cancel(-7t^2)+36t+2t=13+63#

#rArr38t=76#

#"divide both sides by 38"#

#(cancel(38)color(white)(x)t)/cancel(38)=76/38#

#rArrt=2#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides equate then it is the solution.

#"left "=7(4+10-9)+2=(7xx5)+2=37#

#"right "=2(14-2)+13=(2xx12)+13=37#

#rArrt=2" is the solution"#

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Answer 2

Hazel Anglin

To solve the equation 7(t^2 + 5t - 9) + t = t(7t - 2) + 13:

Expand both sides of the equation.
Simplify by combining like terms.
Move all terms to one side of the equation.
Factor if possible.
Solve for the variable t.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.