Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-7)& = & 3 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x-14& = &3+8-x \\\Leftrightarrow & 12x \color{red}{-14} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &11+14 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+5)& = & -6 \color{red}{-} (11+3x) \\\Leftrightarrow & -10x+25& = &-6-11-3x \\\Leftrightarrow & -10x \color{red}{+25} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -10x+3x& = &-17-25 \\\Leftrightarrow & -7x& = &-42 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-42}{ \color{red}{-7} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+7)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & -15x+21& = &-1-5+x \\\Leftrightarrow & -15x \color{red}{+21} & = &-6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -15x-x& = &-6-21 \\\Leftrightarrow & -16x& = &-27 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-27}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{27}{16} & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+4)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x+24& = &-8-14+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-22 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-22-24 \\\Leftrightarrow & 23x& = &-46 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-46}{ \color{red}{23} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+7)& = & 10 \color{red}{+} (12+4x) \\\Leftrightarrow & 3x+21& = &10+12+4x \\\Leftrightarrow & 3x \color{red}{+21} & = &22 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &22 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 3x-4x& = &22-21 \\\Leftrightarrow & -x& = &1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{1}{ \color{red}{-1} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+2)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & 2x+4& = &-10-4-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-14 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-14-4 \\\Leftrightarrow & 3x& = &-18 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-18}{ \color{red}{3} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x+1)& = & -4 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x+2& = &-4+1-x \\\Leftrightarrow & -12x \color{red}{+2} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -12x+x& = &-3-2 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+3)& = & -5 \color{red}{-} (-7+x) \\\Leftrightarrow & 6x+18& = &-5+7-x \\\Leftrightarrow & 6x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &2-18 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-3)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-6& = &4+5+x \\\Leftrightarrow & -12x \color{red}{-6} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &9+6 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x+7)& = & -11 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+28& = &-11+11+3x \\\Leftrightarrow & -4x \color{red}{+28} & = &0 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -4x-3x& = &0-28 \\\Leftrightarrow & -7x& = &-28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-28}{ \color{red}{-7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x-2)& = & 4 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x-8& = &4-9+x \\\Leftrightarrow & 24x \color{red}{-8} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 24x-x& = &-5+8 \\\Leftrightarrow & 23x& = &3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+5)& = & -15 \color{red}{+} (14+x) \\\Leftrightarrow & 18x+15& = &-15+14+x \\\Leftrightarrow & 18x \color{red}{+15} & = &-1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 18x-x& = &-1-15 \\\Leftrightarrow & 17x& = &-16 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-16}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-16}{17} & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)