Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x+2)& = & -14 \color{red}{-} (9+x) \\\Leftrightarrow & 30x+12& = &-14-9-x \\\Leftrightarrow & 30x \color{red}{+12} & = &-23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 30x+x& = &-23-12 \\\Leftrightarrow & 31x& = &-35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-4)& = & 12 \color{red}{-} (1+x) \\\Leftrightarrow & 18x-12& = &12-1-x \\\Leftrightarrow & 18x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &11+12 \\\Leftrightarrow & 19x& = &23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+7)& = & 8 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x+28& = &8-2-3x \\\Leftrightarrow & 4x \color{red}{+28} & = &6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 4x+3x& = &6-28 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-4)& = & -12 \color{red}{-} (-11+x) \\\Leftrightarrow & -25x-20& = &-12+11-x \\\Leftrightarrow & -25x \color{red}{-20} & = &-1 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -25x+x& = &-1+20 \\\Leftrightarrow & -24x& = &19 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{19}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{-19}{24} & & \\ & V = \left\{ \frac{-19}{24} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x+7)& = & 12 \color{red}{+} (-11-5x) \\\Leftrightarrow & 16x+28& = &12-11-5x \\\Leftrightarrow & 16x \color{red}{+28} & = &1 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & 16x+5x& = &1-28 \\\Leftrightarrow & 21x& = &-27 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-27}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-6)& = & 8 \color{red}{+} (1-4x) \\\Leftrightarrow & -5x-30& = &8+1-4x \\\Leftrightarrow & -5x \color{red}{-30} & = &9 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & -5x+4x& = &9+30 \\\Leftrightarrow & -x& = &39 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{39}{ \color{red}{-1} } \\\Leftrightarrow & x = -39 & & \\ & V = \left\{ -39 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+4)& = & 11 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x+24& = &11+2-5x \\\Leftrightarrow & -18x \color{red}{+24} & = &13 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -18x+5x& = &13-24 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+4)& = & -4 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+8& = &-4+13-x \\\Leftrightarrow & 12x \color{red}{+8} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &9-8 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+3)& = & 11 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+12& = &11+5+x \\\Leftrightarrow & 12x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &16-12 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x+4)& = & -2 \color{red}{-} (-10+x) \\\Leftrightarrow & -20x+16& = &-2+10-x \\\Leftrightarrow & -20x \color{red}{+16} & = &8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -20x+x& = &8-16 \\\Leftrightarrow & -19x& = &-8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x-5)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & 4x-20& = &9+7-x \\\Leftrightarrow & 4x \color{red}{-20} & = &16 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &16+20 \\\Leftrightarrow & 5x& = &36 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{36}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{36}{5} & & \\ & V = \left\{ \frac{36}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-7)& = & -14 \color{red}{-} (8-5x) \\\Leftrightarrow & 16x-28& = &-14-8+5x \\\Leftrightarrow & 16x \color{red}{-28} & = &-22 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & 16x-5x& = &-22+28 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)