Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-3)& = & 8 \color{red}{-} (-11+x) \\\Leftrightarrow & -2x-6& = &8+11-x \\\Leftrightarrow & -2x \color{red}{-6} & = &19 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -2x+x& = &19+6 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-4)& = & 3 \color{red}{-} (13-5x) \\\Leftrightarrow & 18x-24& = &3-13+5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 18x-5x& = &-10+24 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x+7)& = & -2 \color{red}{+} (-8+x) \\\Leftrightarrow & 10x+35& = &-2-8+x \\\Leftrightarrow & 10x \color{red}{+35} & = &-10 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 10x-x& = &-10-35 \\\Leftrightarrow & 9x& = &-45 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-45}{ \color{red}{9} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-1)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x-2& = &-10+14-x \\\Leftrightarrow & -6x \color{red}{-2} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -6x+x& = &4+2 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-4x-3)& = & -14 \color{red}{+} (-10+3x) \\\Leftrightarrow & -16x-12& = &-14-10+3x \\\Leftrightarrow & -16x \color{red}{-12} & = &-24 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -16x-3x& = &-24+12 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-4)& = & -5 \color{red}{+} (-13-3x) \\\Leftrightarrow & 4x-8& = &-5-13-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-18+8 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-4)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & 5x-20& = &3-9-x \\\Leftrightarrow & 5x \color{red}{-20} & = &-6 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 5x+x& = &-6+20 \\\Leftrightarrow & 6x& = &14 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{14}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+1)& = & -5 \color{red}{-} (6+x) \\\Leftrightarrow & 20x+5& = &-5-6-x \\\Leftrightarrow & 20x \color{red}{+5} & = &-11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &-11-5 \\\Leftrightarrow & 21x& = &-16 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-16}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-16}{21} & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-7)& = & -5 \color{red}{-} (9+x) \\\Leftrightarrow & -30x-35& = &-5-9-x \\\Leftrightarrow & -30x \color{red}{-35} & = &-14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &-14+35 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+7)& = & -5 \color{red}{+} (-7-5x) \\\Leftrightarrow & 36x+42& = &-5-7-5x \\\Leftrightarrow & 36x \color{red}{+42} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 36x+5x& = &-12-42 \\\Leftrightarrow & 41x& = &-54 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-54}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-54}{41} & & \\ & V = \left\{ \frac{-54}{41} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+1)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+6& = &11-10-x \\\Leftrightarrow & -12x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &1-6 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+3)& = & 1 \color{red}{+} (-6+x) \\\Leftrightarrow & 15x+9& = &1-6+x \\\Leftrightarrow & 15x \color{red}{+9} & = &-5 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 15x-x& = &-5-9 \\\Leftrightarrow & 14x& = &-14 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-14}{ \color{red}{14} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)