Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-6x-1)=-9-(11+x)\)
2. \(6(-5x+1)=15-(13+x)\)
3. \(4(-x-7)=-6-(-11-3x)\)
4. \(2(2x+1)=-7-(-4-3x)\)
5. \(3(x-5)=5+(11+x)\)
6. \(5(-6x-1)=13-(-12+x)\)
7. \(5(6x-1)=8+(11+x)\)
8. \(2(-5x-2)=-2-(-9+x)\)
9. \(3(x-1)=-15+(12+2x)\)
10. \(4(4x+7)=-3+(-10-5x)\)
11. \(3(-4x+2)=15+(3+x)\)
12. \(2(6x-3)=10+(7+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-1)& = & -9 \color{red}{-} (11+x) \\\Leftrightarrow & -18x-3& = &-9-11-x \\\Leftrightarrow & -18x \color{red}{-3} & = &-20 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -18x+x& = &-20+3 \\\Leftrightarrow & -17x& = &-17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-17}{ \color{red}{-17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+1)& = & 15 \color{red}{-} (13+x) \\\Leftrightarrow & -30x+6& = &15-13-x \\\Leftrightarrow & -30x \color{red}{+6} & = &2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -30x+x& = &2-6 \\\Leftrightarrow & -29x& = &-4 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-4}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-7)& = & -6 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x-28& = &-6+11+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &5+28 \\\Leftrightarrow & -7x& = &33 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{33}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-33}{7} & & \\ & V = \left\{ \frac{-33}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+1)& = & -7 \color{red}{-} (-4-3x) \\\Leftrightarrow & 4x+2& = &-7+4+3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 4x-3x& = &-3-2 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-5)& = & 5 \color{red}{+} (11+x) \\\Leftrightarrow & 3x-15& = &5+11+x \\\Leftrightarrow & 3x \color{red}{-15} & = &16 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 3x-x& = &16+15 \\\Leftrightarrow & 2x& = &31 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{31}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{31}{2} & & \\ & V = \left\{ \frac{31}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-1)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x-5& = &13+12-x \\\Leftrightarrow & -30x \color{red}{-5} & = &25 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &25+5 \\\Leftrightarrow & -29x& = &30 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{30}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-30}{29} & & \\ & V = \left\{ \frac{-30}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x-1)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & 30x-5& = &8+11+x \\\Leftrightarrow & 30x \color{red}{-5} & = &19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 30x-x& = &19+5 \\\Leftrightarrow & 29x& = &24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-2)& = & -2 \color{red}{-} (-9+x) \\\Leftrightarrow & -10x-4& = &-2+9-x \\\Leftrightarrow & -10x \color{red}{-4} & = &7 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -10x+x& = &7+4 \\\Leftrightarrow & -9x& = &11 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{11}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-1)& = & -15 \color{red}{+} (12+2x) \\\Leftrightarrow & 3x-3& = &-15+12+2x \\\Leftrightarrow & 3x \color{red}{-3} & = &-3 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 3x-2x& = &-3+3 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+7)& = & -3 \color{red}{+} (-10-5x) \\\Leftrightarrow & 16x+28& = &-3-10-5x \\\Leftrightarrow & 16x \color{red}{+28} & = &-13 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & 16x+5x& = &-13-28 \\\Leftrightarrow & 21x& = &-41 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-41}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-41}{21} & & \\ & V = \left\{ \frac{-41}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+2)& = & 15 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+6& = &15+3+x \\\Leftrightarrow & -12x \color{red}{+6} & = &18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &18-6 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-3)& = & 10 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-6& = &10+7+x \\\Leftrightarrow & 12x \color{red}{-6} & = &17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &17+6 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)