Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-4x+2)=-9+(-1+x)\)
2. \(6(-4x-2)=3+(9+x)\)
3. \(6(-4x+1)=13-(13+x)\)
4. \(5(-x+7)=-7-(11-2x)\)
5. \(4(-4x-3)=-13+(13+3x)\)
6. \(5(-x-2)=12-(-15-4x)\)
7. \(6(5x+3)=-1-(14+x)\)
8. \(3(-4x+5)=9-(14+x)\)
9. \(5(-3x-6)=-14+(-14-2x)\)
10. \(4(6x-6)=7-(-3+x)\)
11. \(5(-x-7)=8-(-4-4x)\)
12. \(5(-5x+4)=9+(7+2x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x+2)& = & -9 \color{red}{+} (-1+x) \\\Leftrightarrow & -24x+12& = &-9-1+x \\\Leftrightarrow & -24x \color{red}{+12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &-10-12 \\\Leftrightarrow & -25x& = &-22 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-22}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{22}{25} & & \\ & V = \left\{ \frac{22}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x-2)& = & 3 \color{red}{+} (9+x) \\\Leftrightarrow & -24x-12& = &3+9+x \\\Leftrightarrow & -24x \color{red}{-12} & = &12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &12+12 \\\Leftrightarrow & -25x& = &24 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{24}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-24}{25} & & \\ & V = \left\{ \frac{-24}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+1)& = & 13 \color{red}{-} (13+x) \\\Leftrightarrow & -24x+6& = &13-13-x \\\Leftrightarrow & -24x \color{red}{+6} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &0-6 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x+7)& = & -7 \color{red}{-} (11-2x) \\\Leftrightarrow & -5x+35& = &-7-11+2x \\\Leftrightarrow & -5x \color{red}{+35} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & -5x-2x& = &-18-35 \\\Leftrightarrow & -7x& = &-53 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-53}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{53}{7} & & \\ & V = \left\{ \frac{53}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-4x-3)& = & -13 \color{red}{+} (13+3x) \\\Leftrightarrow & -16x-12& = &-13+13+3x \\\Leftrightarrow & -16x \color{red}{-12} & = &0 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -16x-3x& = &0+12 \\\Leftrightarrow & -19x& = &12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-2)& = & 12 \color{red}{-} (-15-4x) \\\Leftrightarrow & -5x-10& = &12+15+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &27 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &27+10 \\\Leftrightarrow & -9x& = &37 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{37}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-37}{9} & & \\ & V = \left\{ \frac{-37}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+3)& = & -1 \color{red}{-} (14+x) \\\Leftrightarrow & 30x+18& = &-1-14-x \\\Leftrightarrow & 30x \color{red}{+18} & = &-15 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &-15-18 \\\Leftrightarrow & 31x& = &-33 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-33}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-33}{31} & & \\ & V = \left\{ \frac{-33}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+5)& = & 9 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+15& = &9-14-x \\\Leftrightarrow & -12x \color{red}{+15} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &-5-15 \\\Leftrightarrow & -11x& = &-20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-6)& = & -14 \color{red}{+} (-14-2x) \\\Leftrightarrow & -15x-30& = &-14-14-2x \\\Leftrightarrow & -15x \color{red}{-30} & = &-28 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -15x+2x& = &-28+30 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-6)& = & 7 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x-24& = &7+3-x \\\Leftrightarrow & 24x \color{red}{-24} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &10+24 \\\Leftrightarrow & 25x& = &34 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{34}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{34}{25} & & \\ & V = \left\{ \frac{34}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-7)& = & 8 \color{red}{-} (-4-4x) \\\Leftrightarrow & -5x-35& = &8+4+4x \\\Leftrightarrow & -5x \color{red}{-35} & = &12 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &12 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & -5x-4x& = &12+35 \\\Leftrightarrow & -9x& = &47 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{47}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-47}{9} & & \\ & V = \left\{ \frac{-47}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+4)& = & 9 \color{red}{+} (7+2x) \\\Leftrightarrow & -25x+20& = &9+7+2x \\\Leftrightarrow & -25x \color{red}{+20} & = &16 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -25x-2x& = &16-20 \\\Leftrightarrow & -27x& = &-4 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-4}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)