Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x+2)& = & 4 \color{red}{+} (-6+x) \\\Leftrightarrow & 3x+6& = &4-6+x \\\Leftrightarrow & 3x \color{red}{+6} & = &-2 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 3x-x& = &-2-6 \\\Leftrightarrow & 2x& = &-8 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-8}{ \color{red}{2} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-6)& = & -3 \color{red}{-} (6+2x) \\\Leftrightarrow & 9x-18& = &-3-6-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &-9+18 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-7)& = & -14 \color{red}{-} (1-3x) \\\Leftrightarrow & -4x-28& = &-14-1+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &-15+28 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+1)& = & -15 \color{red}{+} (1-5x) \\\Leftrightarrow & 18x+3& = &-15+1-5x \\\Leftrightarrow & 18x \color{red}{+3} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 18x+5x& = &-14-3 \\\Leftrightarrow & 23x& = &-17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x+4)& = & -12 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+12& = &-12-7+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-19-12 \\\Leftrightarrow & 11x& = &-31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+7)& = & -7 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x+42& = &-7+9-x \\\Leftrightarrow & 12x \color{red}{+42} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 12x+x& = &2-42 \\\Leftrightarrow & 13x& = &-40 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-40}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-40}{13} & & \\ & V = \left\{ \frac{-40}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+2)& = & -8 \color{red}{+} (4-5x) \\\Leftrightarrow & 36x+12& = &-8+4-5x \\\Leftrightarrow & 36x \color{red}{+12} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 36x+5x& = &-4-12 \\\Leftrightarrow & 41x& = &-16 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-16}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-16}{41} & & \\ & V = \left\{ \frac{-16}{41} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-2)& = & -14 \color{red}{-} (1-5x) \\\Leftrightarrow & 3x-6& = &-14-1+5x \\\Leftrightarrow & 3x \color{red}{-6} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 3x-5x& = &-15+6 \\\Leftrightarrow & -2x& = &-9 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-9}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{9}{2} & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x+1)& = & 11 \color{red}{-} (6-2x) \\\Leftrightarrow & -15x+5& = &11-6+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &5 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &5-5 \\\Leftrightarrow & -17x& = &0 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{0}{ \color{red}{-17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-6)& = & 15 \color{red}{-} (6+x) \\\Leftrightarrow & -24x-36& = &15-6-x \\\Leftrightarrow & -24x \color{red}{-36} & = &9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &9+36 \\\Leftrightarrow & -23x& = &45 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{45}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x+3)& = & -6 \color{red}{+} (14-2x) \\\Leftrightarrow & 3x+9& = &-6+14-2x \\\Leftrightarrow & 3x \color{red}{+9} & = &8 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 3x+2x& = &8-9 \\\Leftrightarrow & 5x& = &-1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x-7)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & 36x-42& = &-15+2+x \\\Leftrightarrow & 36x \color{red}{-42} & = &-13 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 36x-x& = &-13+42 \\\Leftrightarrow & 35x& = &29 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{29}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{29}{35} & & \\ & V = \left\{ \frac{29}{35} \right\} & \\\end{align}\)