Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+2)& = & 8 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+6& = &8-4-x \\\Leftrightarrow & -12x \color{red}{+6} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &4-6 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+6)& = & 15 \color{red}{+} (15+2x) \\\Leftrightarrow & -15x+30& = &15+15+2x \\\Leftrightarrow & -15x \color{red}{+30} & = &30 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &30 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -15x-2x& = &30-30 \\\Leftrightarrow & -17x& = &0 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{0}{ \color{red}{-17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x+3)& = & 1 \color{red}{-} (-3-5x) \\\Leftrightarrow & -36x+18& = &1+3+5x \\\Leftrightarrow & -36x \color{red}{+18} & = &4 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -36x-5x& = &4-18 \\\Leftrightarrow & -41x& = &-14 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-14}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{14}{41} & & \\ & V = \left\{ \frac{14}{41} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-3)& = & -13 \color{red}{+} (-7+x) \\\Leftrightarrow & 2x-6& = &-13-7+x \\\Leftrightarrow & 2x \color{red}{-6} & = &-20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 2x-x& = &-20+6 \\\Leftrightarrow & x& = &-14 \\ & V = \left\{ -14 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-4)& = & 13 \color{red}{-} (5+4x) \\\Leftrightarrow & -3x-12& = &13-5-4x \\\Leftrightarrow & -3x \color{red}{-12} & = &8 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & -3x+4x& = &8+12 \\\Leftrightarrow & x& = &20 \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+3)& = & -4 \color{red}{-} (-14-4x) \\\Leftrightarrow & -5x+15& = &-4+14+4x \\\Leftrightarrow & -5x \color{red}{+15} & = &10 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -5x-4x& = &10-15 \\\Leftrightarrow & -9x& = &-5 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-5}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{5}{9} & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x+4)& = & -13 \color{red}{-} (5+x) \\\Leftrightarrow & -15x+12& = &-13-5-x \\\Leftrightarrow & -15x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -15x+x& = &-18-12 \\\Leftrightarrow & -14x& = &-30 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-30}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x+7)& = & -2 \color{red}{-} (-8+x) \\\Leftrightarrow & 36x+42& = &-2+8-x \\\Leftrightarrow & 36x \color{red}{+42} & = &6 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 36x+x& = &6-42 \\\Leftrightarrow & 37x& = &-36 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-36}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-36}{37} & & \\ & V = \left\{ \frac{-36}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+5)& = & 4 \color{red}{-} (-14+3x) \\\Leftrightarrow & -4x+10& = &4+14-3x \\\Leftrightarrow & -4x \color{red}{+10} & = &18 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -4x+3x& = &18-10 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+4)& = & -5 \color{red}{-} (12+x) \\\Leftrightarrow & 30x+20& = &-5-12-x \\\Leftrightarrow & 30x \color{red}{+20} & = &-17 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &-17-20 \\\Leftrightarrow & 31x& = &-37 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-37}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-37}{31} & & \\ & V = \left\{ \frac{-37}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x+7)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & 18x+42& = &6-3+x \\\Leftrightarrow & 18x \color{red}{+42} & = &3 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 18x-x& = &3-42 \\\Leftrightarrow & 17x& = &-39 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-39}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-39}{17} & & \\ & V = \left\{ \frac{-39}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+6)& = & 15 \color{red}{-} (-4+x) \\\Leftrightarrow & -18x+36& = &15+4-x \\\Leftrightarrow & -18x \color{red}{+36} & = &19 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -18x+x& = &19-36 \\\Leftrightarrow & -17x& = &-17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-17}{ \color{red}{-17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)