Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+1)& = & -14 \color{red}{-} (14-4x) \\\Leftrightarrow & -9x+3& = &-14-14+4x \\\Leftrightarrow & -9x \color{red}{+3} & = &-28 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &-28 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & -9x-4x& = &-28-3 \\\Leftrightarrow & -13x& = &-31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-6)& = & 12 \color{red}{+} (-9+2x) \\\Leftrightarrow & 25x-30& = &12-9+2x \\\Leftrightarrow & 25x \color{red}{-30} & = &3 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & 25x-2x& = &3+30 \\\Leftrightarrow & 23x& = &33 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{33}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{33}{23} & & \\ & V = \left\{ \frac{33}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+6)& = & -11 \color{red}{-} (13+3x) \\\Leftrightarrow & -4x+12& = &-11-13-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &-24 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &-24-12 \\\Leftrightarrow & -x& = &-36 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-36}{ \color{red}{-1} } \\\Leftrightarrow & x = 36 & & \\ & V = \left\{ 36 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-5)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & -25x-25& = &14-7+x \\\Leftrightarrow & -25x \color{red}{-25} & = &7 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -25x-x& = &7+25 \\\Leftrightarrow & -26x& = &32 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{32}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-2)& = & 12 \color{red}{+} (-14-5x) \\\Leftrightarrow & -3x-6& = &12-14-5x \\\Leftrightarrow & -3x \color{red}{-6} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -3x+5x& = &-2+6 \\\Leftrightarrow & 2x& = &4 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{4}{ \color{red}{2} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+4)& = & -7 \color{red}{+} (4-5x) \\\Leftrightarrow & 6x+24& = &-7+4-5x \\\Leftrightarrow & 6x \color{red}{+24} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 6x+5x& = &-3-24 \\\Leftrightarrow & 11x& = &-27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+3)& = & -2 \color{red}{+} (-13-5x) \\\Leftrightarrow & -18x+18& = &-2-13-5x \\\Leftrightarrow & -18x \color{red}{+18} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -18x+5x& = &-15-18 \\\Leftrightarrow & -13x& = &-33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+6)& = & 4 \color{red}{+} (-6-5x) \\\Leftrightarrow & -16x+24& = &4-6-5x \\\Leftrightarrow & -16x \color{red}{+24} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -16x+5x& = &-2-24 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-5)& = & 11 \color{red}{-} (-7+x) \\\Leftrightarrow & -2x-10& = &11+7-x \\\Leftrightarrow & -2x \color{red}{-10} & = &18 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -2x+x& = &18+10 \\\Leftrightarrow & -x& = &28 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{28}{ \color{red}{-1} } \\\Leftrightarrow & x = -28 & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x-6)& = & -5 \color{red}{-} (-9+x) \\\Leftrightarrow & 16x-24& = &-5+9-x \\\Leftrightarrow & 16x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &4+24 \\\Leftrightarrow & 17x& = &28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+7)& = & -6 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x+28& = &-6+13-x \\\Leftrightarrow & -20x \color{red}{+28} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &7-28 \\\Leftrightarrow & -19x& = &-21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-2)& = & 15 \color{red}{+} (13-2x) \\\Leftrightarrow & -9x-6& = &15+13-2x \\\Leftrightarrow & -9x \color{red}{-6} & = &28 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -9x+2x& = &28+6 \\\Leftrightarrow & -7x& = &34 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{34}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-34}{7} & & \\ & V = \left\{ \frac{-34}{7} \right\} & \\\end{align}\)