Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x-5)& = & -8 \color{red}{+} (-12+3x) \\\Leftrightarrow & 8x-10& = &-8-12+3x \\\Leftrightarrow & 8x \color{red}{-10} & = &-20 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 8x-3x& = &-20+10 \\\Leftrightarrow & 5x& = &-10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-10}{ \color{red}{5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-3)& = & 7 \color{red}{-} (8+x) \\\Leftrightarrow & -6x-18& = &7-8-x \\\Leftrightarrow & -6x \color{red}{-18} & = &-1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -6x+x& = &-1+18 \\\Leftrightarrow & -5x& = &17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+1)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & 12x+2& = &14+15+x \\\Leftrightarrow & 12x \color{red}{+2} & = &29 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &29-2 \\\Leftrightarrow & 11x& = &27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{27}{11} & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+7)& = & 15 \color{red}{+} (-8+3x) \\\Leftrightarrow & 4x+28& = &15-8+3x \\\Leftrightarrow & 4x \color{red}{+28} & = &7 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 4x-3x& = &7-28 \\\Leftrightarrow & x& = &-21 \\ & V = \left\{ -21 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+6)& = & -5 \color{red}{-} (-4+3x) \\\Leftrightarrow & 4x+24& = &-5+4-3x \\\Leftrightarrow & 4x \color{red}{+24} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 4x+3x& = &-1-24 \\\Leftrightarrow & 7x& = &-25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+3)& = & 11 \color{red}{+} (-7+x) \\\Leftrightarrow & 24x+18& = &11-7+x \\\Leftrightarrow & 24x \color{red}{+18} & = &4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 24x-x& = &4-18 \\\Leftrightarrow & 23x& = &-14 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-14}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-14}{23} & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-7)& = & 7 \color{red}{-} (11+x) \\\Leftrightarrow & 8x-28& = &7-11-x \\\Leftrightarrow & 8x \color{red}{-28} & = &-4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 8x+x& = &-4+28 \\\Leftrightarrow & 9x& = &24 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{24}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-5)& = & 12 \color{red}{-} (7+x) \\\Leftrightarrow & 20x-25& = &12-7-x \\\Leftrightarrow & 20x \color{red}{-25} & = &5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 20x+x& = &5+25 \\\Leftrightarrow & 21x& = &30 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{30}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-2)& = & 9 \color{red}{-} (-13+x) \\\Leftrightarrow & 8x-4& = &9+13-x \\\Leftrightarrow & 8x \color{red}{-4} & = &22 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &22+4 \\\Leftrightarrow & 9x& = &26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{26}{9} & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-1)& = & 13 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-2& = &13-2-x \\\Leftrightarrow & 12x \color{red}{-2} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &11+2 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+1)& = & 3 \color{red}{-} (-4-4x) \\\Leftrightarrow & -5x+5& = &3+4+4x \\\Leftrightarrow & -5x \color{red}{+5} & = &7 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & -5x-4x& = &7-5 \\\Leftrightarrow & -9x& = &2 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{2}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x-5)& = & -15 \color{red}{+} (-10-5x) \\\Leftrightarrow & -6x-10& = &-15-10-5x \\\Leftrightarrow & -6x \color{red}{-10} & = &-25 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -6x+5x& = &-25+10 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)