Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x+7)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & -20x+35& = &-15+2+x \\\Leftrightarrow & -20x \color{red}{+35} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -20x-x& = &-13-35 \\\Leftrightarrow & -21x& = &-48 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-48}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+3)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & 16x+12& = &-6+7+x \\\Leftrightarrow & 16x \color{red}{+12} & = &1 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 16x-x& = &1-12 \\\Leftrightarrow & 15x& = &-11 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-11}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-11}{15} & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x-4)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-24& = &3-14-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-11+24 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-2x+5)& = & 7 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+30& = &7-12+x \\\Leftrightarrow & -12x \color{red}{+30} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -12x-x& = &-5-30 \\\Leftrightarrow & -13x& = &-35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+4)& = & -8 \color{red}{+} (3+x) \\\Leftrightarrow & 3x+12& = &-8+3+x \\\Leftrightarrow & 3x \color{red}{+12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 3x-x& = &-5-12 \\\Leftrightarrow & 2x& = &-17 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-17}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-17}{2} & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+5)& = & -4 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x+30& = &-4-11+x \\\Leftrightarrow & 12x \color{red}{+30} & = &-15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 12x-x& = &-15-30 \\\Leftrightarrow & 11x& = &-45 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-45}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-45}{11} & & \\ & V = \left\{ \frac{-45}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+5)& = & 14 \color{red}{-} (-10-2x) \\\Leftrightarrow & 5x+25& = &14+10+2x \\\Leftrightarrow & 5x \color{red}{+25} & = &24 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &24 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & 5x-2x& = &24-25 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x+7)& = & 6 \color{red}{+} (-13+3x) \\\Leftrightarrow & 10x+35& = &6-13+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &-7-35 \\\Leftrightarrow & 7x& = &-42 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-42}{ \color{red}{7} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-6)& = & -1 \color{red}{+} (-7-2x) \\\Leftrightarrow & 3x-18& = &-1-7-2x \\\Leftrightarrow & 3x \color{red}{-18} & = &-8 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 3x+2x& = &-8+18 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-3)& = & 4 \color{red}{-} (11+4x) \\\Leftrightarrow & -15x-9& = &4-11-4x \\\Leftrightarrow & -15x \color{red}{-9} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & -15x+4x& = &-7+9 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x-2)& = & 11 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-8& = &11-6+x \\\Leftrightarrow & 12x \color{red}{-8} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &5+8 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x-6)& = & -6 \color{red}{+} (6-5x) \\\Leftrightarrow & -18x-18& = &-6+6-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &0 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &0+18 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)