Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x+6)& = & -13 \color{red}{-} (-2+x) \\\Leftrightarrow & 24x+36& = &-13+2-x \\\Leftrightarrow & 24x \color{red}{+36} & = &-11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &-11-36 \\\Leftrightarrow & 25x& = &-47 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-47}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-47}{25} & & \\ & V = \left\{ \frac{-47}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x-5)& = & -8 \color{red}{-} (-15-2x) \\\Leftrightarrow & -15x-15& = &-8+15+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &7 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &7+15 \\\Leftrightarrow & -17x& = &22 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{22}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-22}{17} & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x+3)& = & -6 \color{red}{+} (-10+x) \\\Leftrightarrow & -6x+18& = &-6-10+x \\\Leftrightarrow & -6x \color{red}{+18} & = &-16 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -6x-x& = &-16-18 \\\Leftrightarrow & -7x& = &-34 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-34}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{34}{7} & & \\ & V = \left\{ \frac{34}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+7)& = & -8 \color{red}{-} (9+x) \\\Leftrightarrow & -6x+21& = &-8-9-x \\\Leftrightarrow & -6x \color{red}{+21} & = &-17 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -6x+x& = &-17-21 \\\Leftrightarrow & -5x& = &-38 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-38}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{38}{5} & & \\ & V = \left\{ \frac{38}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+7)& = & 10 \color{red}{-} (-3+4x) \\\Leftrightarrow & 15x+21& = &10+3-4x \\\Leftrightarrow & 15x \color{red}{+21} & = &13 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 15x+4x& = &13-21 \\\Leftrightarrow & 19x& = &-8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+4)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+16& = &9+4+x \\\Leftrightarrow & 12x \color{red}{+16} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 12x-x& = &13-16 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+7)& = & 14 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+21& = &14-4-x \\\Leftrightarrow & -12x \color{red}{+21} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &10-21 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+1)& = & 3 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x+6& = &3+5-x \\\Leftrightarrow & -24x \color{red}{+6} & = &8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &8-6 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x-5)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & -10x-25& = &-5+11+x \\\Leftrightarrow & -10x \color{red}{-25} & = &6 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -10x-x& = &6+25 \\\Leftrightarrow & -11x& = &31 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{31}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+4)& = & 4 \color{red}{+} (-8+x) \\\Leftrightarrow & 36x+24& = &4-8+x \\\Leftrightarrow & 36x \color{red}{+24} & = &-4 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 36x-x& = &-4-24 \\\Leftrightarrow & 35x& = &-28 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-28}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x-3)& = & 9 \color{red}{+} (15+x) \\\Leftrightarrow & 15x-15& = &9+15+x \\\Leftrightarrow & 15x \color{red}{-15} & = &24 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 15x-x& = &24+15 \\\Leftrightarrow & 14x& = &39 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{39}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{39}{14} & & \\ & V = \left\{ \frac{39}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x+7)& = & -8 \color{red}{+} (-2+3x) \\\Leftrightarrow & 2x+14& = &-8-2+3x \\\Leftrightarrow & 2x \color{red}{+14} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 2x-3x& = &-10-14 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)