Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x-7)& = & -4 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-28& = &-4-14-x \\\Leftrightarrow & -12x \color{red}{-28} & = &-18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -12x+x& = &-18+28 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+1)& = & -4 \color{red}{-} (-9+3x) \\\Leftrightarrow & 8x+4& = &-4+9-3x \\\Leftrightarrow & 8x \color{red}{+4} & = &5 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 8x+3x& = &5-4 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+6)& = & 1 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+18& = &1-14-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-13-18 \\\Leftrightarrow & 13x& = &-31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-7)& = & -4 \color{red}{+} (-15+x) \\\Leftrightarrow & 6x-42& = &-4-15+x \\\Leftrightarrow & 6x \color{red}{-42} & = &-19 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 6x-x& = &-19+42 \\\Leftrightarrow & 5x& = &23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{23}{5} & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+2)& = & 5 \color{red}{-} (10-3x) \\\Leftrightarrow & 4x+8& = &5-10+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &-5-8 \\\Leftrightarrow & x& = &-13 \\ & V = \left\{ -13 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-2)& = & 4 \color{red}{+} (-3+4x) \\\Leftrightarrow & 9x-6& = &4-3+4x \\\Leftrightarrow & 9x \color{red}{-6} & = &1 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & 9x-4x& = &1+6 \\\Leftrightarrow & 5x& = &7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+7)& = & -4 \color{red}{-} (-7+x) \\\Leftrightarrow & -16x+28& = &-4+7-x \\\Leftrightarrow & -16x \color{red}{+28} & = &3 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -16x+x& = &3-28 \\\Leftrightarrow & -15x& = &-25 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-25}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x-7)& = & -7 \color{red}{-} (13-3x) \\\Leftrightarrow & -4x-14& = &-7-13+3x \\\Leftrightarrow & -4x \color{red}{-14} & = &-20 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -4x-3x& = &-20+14 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+5)& = & 13 \color{red}{-} (4+3x) \\\Leftrightarrow & -10x+25& = &13-4-3x \\\Leftrightarrow & -10x \color{red}{+25} & = &9 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -10x+3x& = &9-25 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+4)& = & 3 \color{red}{-} (7+x) \\\Leftrightarrow & -6x+12& = &3-7-x \\\Leftrightarrow & -6x \color{red}{+12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &-4-12 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-2)& = & 2 \color{red}{-} (10+2x) \\\Leftrightarrow & 15x-6& = &2-10-2x \\\Leftrightarrow & 15x \color{red}{-6} & = &-8 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & 15x+2x& = &-8+6 \\\Leftrightarrow & 17x& = &-2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-5)& = & 15 \color{red}{-} (5+x) \\\Leftrightarrow & 12x-30& = &15-5-x \\\Leftrightarrow & 12x \color{red}{-30} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 12x+x& = &10+30 \\\Leftrightarrow & 13x& = &40 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{40}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{40}{13} & & \\ & V = \left\{ \frac{40}{13} \right\} & \\\end{align}\)