Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-5)& = & 6 \color{red}{+} (-10+x) \\\Leftrightarrow & -25x-25& = &6-10+x \\\Leftrightarrow & -25x \color{red}{-25} & = &-4 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -25x-x& = &-4+25 \\\Leftrightarrow & -26x& = &21 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{21}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-21}{26} & & \\ & V = \left\{ \frac{-21}{26} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+5)& = & -12 \color{red}{+} (-15+x) \\\Leftrightarrow & -4x+20& = &-12-15+x \\\Leftrightarrow & -4x \color{red}{+20} & = &-27 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -4x-x& = &-27-20 \\\Leftrightarrow & -5x& = &-47 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-47}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{47}{5} & & \\ & V = \left\{ \frac{47}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x-1)& = & -3 \color{red}{+} (7-3x) \\\Leftrightarrow & -4x-2& = &-3+7-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &4+2 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+3)& = & -5 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x+6& = &-5-9+x \\\Leftrightarrow & 2x \color{red}{+6} & = &-14 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 2x-x& = &-14-6 \\\Leftrightarrow & x& = &-20 \\ & V = \left\{ -20 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+1)& = & 1 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+6& = &1-15+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-14-6 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-2)& = & -4 \color{red}{-} (10-4x) \\\Leftrightarrow & -25x-10& = &-4-10+4x \\\Leftrightarrow & -25x \color{red}{-10} & = &-14 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -25x-4x& = &-14+10 \\\Leftrightarrow & -29x& = &-4 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-4}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+5)& = & 4 \color{red}{+} (8+x) \\\Leftrightarrow & -5x+25& = &4+8+x \\\Leftrightarrow & -5x \color{red}{+25} & = &12 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -5x-x& = &12-25 \\\Leftrightarrow & -6x& = &-13 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-13}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{13}{6} & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+7)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & 24x+28& = &5+6+x \\\Leftrightarrow & 24x \color{red}{+28} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &11-28 \\\Leftrightarrow & 23x& = &-17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-7)& = & 9 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-42& = &9-14+x \\\Leftrightarrow & -12x \color{red}{-42} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &-5+42 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x+2)& = & 8 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+4& = &8+5+x \\\Leftrightarrow & 12x \color{red}{+4} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &13-4 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+5)& = & 14 \color{red}{-} (-8+x) \\\Leftrightarrow & -30x+30& = &14+8-x \\\Leftrightarrow & -30x \color{red}{+30} & = &22 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &22-30 \\\Leftrightarrow & -29x& = &-8 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-8}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+5)& = & 7 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+15& = &7-4+x \\\Leftrightarrow & -12x \color{red}{+15} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -12x-x& = &3-15 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)