Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-2)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & -15x-6& = &9+4+x \\\Leftrightarrow & -15x \color{red}{-6} & = &13 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -15x-x& = &13+6 \\\Leftrightarrow & -16x& = &19 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{19}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-19}{16} & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+4)& = & 8 \color{red}{+} (11-2x) \\\Leftrightarrow & -5x+20& = &8+11-2x \\\Leftrightarrow & -5x \color{red}{+20} & = &19 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -5x+2x& = &19-20 \\\Leftrightarrow & -3x& = &-1 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-1}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-6)& = & 13 \color{red}{-} (-4-3x) \\\Leftrightarrow & 25x-30& = &13+4+3x \\\Leftrightarrow & 25x \color{red}{-30} & = &17 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 25x-3x& = &17+30 \\\Leftrightarrow & 22x& = &47 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{47}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{47}{22} & & \\ & V = \left\{ \frac{47}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x+4)& = & -3 \color{red}{-} (8+x) \\\Leftrightarrow & 8x+16& = &-3-8-x \\\Leftrightarrow & 8x \color{red}{+16} & = &-11 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 8x+x& = &-11-16 \\\Leftrightarrow & 9x& = &-27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-27}{ \color{red}{9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+4)& = & -3 \color{red}{+} (-9+x) \\\Leftrightarrow & 4x+8& = &-3-9+x \\\Leftrightarrow & 4x \color{red}{+8} & = &-12 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &-12-8 \\\Leftrightarrow & 3x& = &-20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-7)& = & 13 \color{red}{-} (6+3x) \\\Leftrightarrow & 8x-28& = &13-6-3x \\\Leftrightarrow & 8x \color{red}{-28} & = &7 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 8x+3x& = &7+28 \\\Leftrightarrow & 11x& = &35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x+1)& = & -1 \color{red}{+} (-1+x) \\\Leftrightarrow & -25x+5& = &-1-1+x \\\Leftrightarrow & -25x \color{red}{+5} & = &-2 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -25x-x& = &-2-5 \\\Leftrightarrow & -26x& = &-7 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-7}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{7}{26} & & \\ & V = \left\{ \frac{7}{26} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+7)& = & 13 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x+42& = &13+11-x \\\Leftrightarrow & 24x \color{red}{+42} & = &24 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &24-42 \\\Leftrightarrow & 25x& = &-18 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-18}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-18}{25} & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-2)& = & -15 \color{red}{+} (-4-5x) \\\Leftrightarrow & 18x-6& = &-15-4-5x \\\Leftrightarrow & 18x \color{red}{-6} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 18x+5x& = &-19+6 \\\Leftrightarrow & 23x& = &-13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+6)& = & -3 \color{red}{+} (3+x) \\\Leftrightarrow & 8x+24& = &-3+3+x \\\Leftrightarrow & 8x \color{red}{+24} & = &0 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 8x-x& = &0-24 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x+3)& = & 14 \color{red}{-} (-14+x) \\\Leftrightarrow & 8x+6& = &14+14-x \\\Leftrightarrow & 8x \color{red}{+6} & = &28 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 8x+x& = &28-6 \\\Leftrightarrow & 9x& = &22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-6)& = & 11 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x-36& = &11+13+5x \\\Leftrightarrow & 6x \color{red}{-36} & = &24 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & 6x-5x& = &24+36 \\\Leftrightarrow & x& = &60 \\ & V = \left\{ 60 \right\} & \\\end{align}\)