Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-5)& = & -15 \color{red}{+} (10-3x) \\\Leftrightarrow & 4x-10& = &-15+10-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &-5+10 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+4)& = & -5 \color{red}{-} (13+x) \\\Leftrightarrow & 6x+12& = &-5-13-x \\\Leftrightarrow & 6x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &-18-12 \\\Leftrightarrow & 7x& = &-30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x+7)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & 15x+21& = &-7-7+x \\\Leftrightarrow & 15x \color{red}{+21} & = &-14 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 15x-x& = &-14-21 \\\Leftrightarrow & 14x& = &-35 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-35}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-4)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & 20x-20& = &6+9+x \\\Leftrightarrow & 20x \color{red}{-20} & = &15 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &15+20 \\\Leftrightarrow & 19x& = &35 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{35}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-6)& = & -14 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x-18& = &-14-11-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &-25 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &-25+18 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+4)& = & -14 \color{red}{+} (-1+x) \\\Leftrightarrow & -8x+8& = &-14-1+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-15-8 \\\Leftrightarrow & -9x& = &-23 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-23}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-4)& = & -8 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-24& = &-8-8-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-16+24 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-1)& = & -12 \color{red}{-} (10-3x) \\\Leftrightarrow & 4x-4& = &-12-10+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &-22+4 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-7)& = & 11 \color{red}{+} (7+x) \\\Leftrightarrow & 4x-14& = &11+7+x \\\Leftrightarrow & 4x \color{red}{-14} & = &18 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 4x-x& = &18+14 \\\Leftrightarrow & 3x& = &32 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{32}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{32}{3} & & \\ & V = \left\{ \frac{32}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+3)& = & 10 \color{red}{+} (1+4x) \\\Leftrightarrow & 15x+9& = &10+1+4x \\\Leftrightarrow & 15x \color{red}{+9} & = &11 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 15x-4x& = &11-9 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-3)& = & -2 \color{red}{+} (5+4x) \\\Leftrightarrow & -3x-9& = &-2+5+4x \\\Leftrightarrow & -3x \color{red}{-9} & = &3 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & -3x-4x& = &3+9 \\\Leftrightarrow & -7x& = &12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+6)& = & 14 \color{red}{+} (-4-4x) \\\Leftrightarrow & 25x+30& = &14-4-4x \\\Leftrightarrow & 25x \color{red}{+30} & = &10 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 25x+4x& = &10-30 \\\Leftrightarrow & 29x& = &-20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-20}{29} & & \\ & V = \left\{ \frac{-20}{29} \right\} & \\\end{align}\)