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chapter9.3b
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à 9.3êïIntroduction to Solving Equations.
äë Please solve the following equations.
â
êêêèSolve.ë x - 7 = 4
êêêêëx + (-7) = 4
ë Add 7 to both sides.êë 7è 7
#êêêêë────────────
êêêêëxê = 11
êêë The solution to this equation is 11.
éSèSolving an equation means to find the number that makes a true
sentence out of the original equation when the number is substituted in
place of the variable.ïIn order to solve the equation, x - 7 = 4, you
should first change all subtractions to addition.
êêêêx + (-7) = 4
Then, add the opposite of "-7" to both sides of the equation.
êêêêx + (-7) = 4
êêêêë 7è 7
#êêêê────────────
êêêêxê= 11
This has the effect of isolating "x". The solution is the number on the
other side of the equation.ïThe solution is "11".ïEleven is the number
that makes a true sentence out of the original equation.
êêêê 11 - 7 = 4
êêêêë 4 = 4
This is the check to make sure you have the correct solution.
1
êêè Solve the equation,è x - 3 = 14.
êïA)ï-11êB)ï17êC)ï11ê D)ïå
ü
êêêêë x - 3 = 14
êêêêèx + (-3) = 14
èAdd 3 to both sides.êê3ë3
#êêêêè─────────────
êêêêèxê = 17
êêêêThe solution is 17.
Ç B
2
êêè Solve the equation,è x + 8 = 14.
êïA)ï-12êB)ï5ê C)ï6êïD)ïå
ü
êêêêë x + 8 = 14
èAdd -8 to both sides.êë -8è-8
#êêêêë───────────
êêêêë xë=ï6
êêêêïThe solution is 6.
Ç C
3
êêè Solve the equation,è x - 14 = -9
êïA)ï-6ê B)ï5ê C)ï7êïD)ïå
ü
êêêêë x - 14 = -9
êêêêëx + (-14) = -9
èAdd 14 to both sides.êê 14è 14
#êêêêë──────────────
êêêêë xêï= 5
êêêêïThe solution is 5.
Ç B
4
êêè Solve the equation,è x + 16 = 10
êïA)ï-6ê B)ï26êC)ï6êïD)ïå
ü
êêêêë x + 16 =ï10
èAdd -16 to both sides.êë-16è-16
#êêêêë──────────────
êêêêë xë =ï-6
êêêêïThe solution is -6.
Ç A
5
êêêêêë x
#êêè Solve the equation,è ─ï=ï4 .
êêêêêë 3
êïA)ï-1ê B)ï7ê C)ï12ê D)ïå
üêêêêx
#êêêêë───ï=ï4
êêêêë 3
êêêêêx
# Multiply both sides by "3".è 3∙───ï=ï3∙4
êêêêê3
êêêêëxï=ï12
Ç C
6
êêêêêë x
#êêè Solve the equation,è───ï=ï12 .
êêêêêë-6
êïA)ï2êïB)ï-72ë C)ï-2ê D)ïå
üêêêêx
#êêêêë───ï=ï12
êêêêë-6
êêêêêx
#Multiply both sides by "-6".è-6∙───ï=ï-6∙12
êêêêë -6
êêêêëxï=ï-72
Ç B
7
êêè Solve the equation,è4xï=ï24 .
êïA)ï28ê B)ï96êC)ï6êïD)ïå
ü
êêêêêï4xï=ï24
Multiply both sides by 1/4.è(1/4)∙4 xï=ï(1/4)∙24
êêêêêïxï=ï6
êêêêè The solution is 6.
Ç C
8
êêëSolve the equation,è-2xï=ï14
êïA)ï-7ê B)ï28êC)ï16ê D)ïå
ü
êêêêêë-2xï=ï14
Multiply both sides by (-1/2).è(-1/2)∙2 xï=ï(-1/2)∙14
êêêêêêxï=ï-7
êêêêê The solution is -7.
Ç A
9
êêè Solve the equation,è2x + 6ï=ï20.
êïA)ï-12êB)ï7ê C)ï14ê D)ïå
üêêêêê 2x + 6ï=ï20
ê Add "-6" to both sides.è 2x + 6 + (-6)ï=ï20 + (-6)
êêêêêêè2xè=è14
Multiply both sides by (1/2).êè(1/2)∙2 xï=ï(1/2)∙14
êêêêêêëxï=ï7
êêêêêïThe solution is 7.
Ç B
10
êêè Solve the equation,è4x - 12ï=ï20.
êïA)ï14ê B)ï-6êC)ï8êïD)ïå
üêêêêê 4x - 12ï=ï20
êêêêêë4x + (-12)ï=ï20
ê Add "12" to both sides.è 4x + (-12) + 12ï=ï20 + 12
êêêêêêï4xè=è32
Multiply both sides by (1/4).êè(1/4)∙4 xï=ï(1/4)∙32
êêêêêêëxï=ï8
êêêêêë The solution is 8.
Ç C