Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+7)& = & -1 \color{red}{+} (-7+x) \\\Leftrightarrow & 16x+28& = &-1-7+x \\\Leftrightarrow & 16x \color{red}{+28} & = &-8 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 16x-x& = &-8-28 \\\Leftrightarrow & 15x& = &-36 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-36}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-3)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-12& = &-13+15+x \\\Leftrightarrow & -12x \color{red}{-12} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &2+12 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-3)& = & 4 \color{red}{+} (-1-2x) \\\Leftrightarrow & 15x-15& = &4-1-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &3 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &3+15 \\\Leftrightarrow & 17x& = &18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+6)& = & -2 \color{red}{-} (-2-2x) \\\Leftrightarrow & -15x+30& = &-2+2+2x \\\Leftrightarrow & -15x \color{red}{+30} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -15x-2x& = &0-30 \\\Leftrightarrow & -17x& = &-30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x-7)& = & 6 \color{red}{+} (1-5x) \\\Leftrightarrow & 18x-42& = &6+1-5x \\\Leftrightarrow & 18x \color{red}{-42} & = &7 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 18x+5x& = &7+42 \\\Leftrightarrow & 23x& = &49 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{49}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{49}{23} & & \\ & V = \left\{ \frac{49}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+4)& = & -3 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+8& = &-3+2-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-1-8 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+1)& = & -2 \color{red}{+} (1+x) \\\Leftrightarrow & 24x+6& = &-2+1+x \\\Leftrightarrow & 24x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 24x-x& = &-1-6 \\\Leftrightarrow & 23x& = &-7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-2)& = & -4 \color{red}{+} (-15-3x) \\\Leftrightarrow & 4x-8& = &-4-15-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-19+8 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+2)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & -25x+10& = &1+4+x \\\Leftrightarrow & -25x \color{red}{+10} & = &5 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -25x-x& = &5-10 \\\Leftrightarrow & -26x& = &-5 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-5}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{5}{26} & & \\ & V = \left\{ \frac{5}{26} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-1)& = & 11 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x-3& = &11-15+x \\\Leftrightarrow & 18x \color{red}{-3} & = &-4 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 18x-x& = &-4+3 \\\Leftrightarrow & 17x& = &-1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-7)& = & 13 \color{red}{+} (-7+x) \\\Leftrightarrow & 18x-21& = &13-7+x \\\Leftrightarrow & 18x \color{red}{-21} & = &6 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &6+21 \\\Leftrightarrow & 17x& = &27 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{27}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{27}{17} & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-1)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & 16x-4& = &-1+5-x \\\Leftrightarrow & 16x \color{red}{-4} & = &4 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 16x+x& = &4+4 \\\Leftrightarrow & 17x& = &8 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{8}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)