Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+7)& = & -13 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x+42& = &-13-12-5x \\\Leftrightarrow & -6x \color{red}{+42} & = &-25 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -6x+5x& = &-25-42 \\\Leftrightarrow & -x& = &-67 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-67}{ \color{red}{-1} } \\\Leftrightarrow & x = 67 & & \\ & V = \left\{ 67 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+2)& = & -4 \color{red}{-} (7+3x) \\\Leftrightarrow & 8x+8& = &-4-7-3x \\\Leftrightarrow & 8x \color{red}{+8} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 8x+3x& = &-11-8 \\\Leftrightarrow & 11x& = &-19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-4)& = & 10 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-16& = &10-11-x \\\Leftrightarrow & 12x \color{red}{-16} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &-1+16 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-2)& = & -10 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x-12& = &-10+6-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-4+12 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-1)& = & -11 \color{red}{-} (-10-3x) \\\Leftrightarrow & -4x-4& = &-11+10+3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -4x-3x& = &-1+4 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-2)& = & -2 \color{red}{+} (9+4x) \\\Leftrightarrow & 9x-6& = &-2+9+4x \\\Leftrightarrow & 9x \color{red}{-6} & = &7 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & 9x-4x& = &7+6 \\\Leftrightarrow & 5x& = &13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+7)& = & -9 \color{red}{+} (7+x) \\\Leftrightarrow & -16x+28& = &-9+7+x \\\Leftrightarrow & -16x \color{red}{+28} & = &-2 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -16x-x& = &-2-28 \\\Leftrightarrow & -17x& = &-30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x-1)& = & -8 \color{red}{+} (-10+x) \\\Leftrightarrow & 36x-6& = &-8-10+x \\\Leftrightarrow & 36x \color{red}{-6} & = &-18 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 36x-x& = &-18+6 \\\Leftrightarrow & 35x& = &-12 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-12}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-7)& = & -6 \color{red}{+} (11+x) \\\Leftrightarrow & 24x-42& = &-6+11+x \\\Leftrightarrow & 24x \color{red}{-42} & = &5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &5+42 \\\Leftrightarrow & 23x& = &47 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{47}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-1)& = & -15 \color{red}{-} (-12-3x) \\\Leftrightarrow & 4x-4& = &-15+12+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &-3+4 \\\Leftrightarrow & x& = &1 \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+7)& = & -5 \color{red}{+} (-14-2x) \\\Leftrightarrow & -25x+35& = &-5-14-2x \\\Leftrightarrow & -25x \color{red}{+35} & = &-19 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -25x+2x& = &-19-35 \\\Leftrightarrow & -23x& = &-54 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-54}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{54}{23} & & \\ & V = \left\{ \frac{54}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+6)& = & -11 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x+12& = &-11-5+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-16-12 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)