Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x+2)& = & -1 \color{red}{+} (8+x) \\\Leftrightarrow & -20x+10& = &-1+8+x \\\Leftrightarrow & -20x \color{red}{+10} & = &7 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &7-10 \\\Leftrightarrow & -21x& = &-3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x+2)& = & -9 \color{red}{-} (3+x) \\\Leftrightarrow & 8x+4& = &-9-3-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-12 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-12-4 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+4)& = & -3 \color{red}{+} (11+x) \\\Leftrightarrow & 16x+16& = &-3+11+x \\\Leftrightarrow & 16x \color{red}{+16} & = &8 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 16x-x& = &8-16 \\\Leftrightarrow & 15x& = &-8 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-8}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-2)& = & 10 \color{red}{+} (15-5x) \\\Leftrightarrow & -18x-12& = &10+15-5x \\\Leftrightarrow & -18x \color{red}{-12} & = &25 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -18x+5x& = &25+12 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+4)& = & 8 \color{red}{-} (-6+x) \\\Leftrightarrow & 10x+20& = &8+6-x \\\Leftrightarrow & 10x \color{red}{+20} & = &14 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 10x+x& = &14-20 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-3)& = & 13 \color{red}{-} (6-5x) \\\Leftrightarrow & -36x-18& = &13-6+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &7 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &7+18 \\\Leftrightarrow & -41x& = &25 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{25}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-25}{41} & & \\ & V = \left\{ \frac{-25}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+1)& = & -12 \color{red}{-} (12+x) \\\Leftrightarrow & -20x+5& = &-12-12-x \\\Leftrightarrow & -20x \color{red}{+5} & = &-24 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -20x+x& = &-24-5 \\\Leftrightarrow & -19x& = &-29 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-29}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x-1)& = & 13 \color{red}{-} (6+x) \\\Leftrightarrow & 12x-4& = &13-6-x \\\Leftrightarrow & 12x \color{red}{-4} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &7+4 \\\Leftrightarrow & 13x& = &11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x+4)& = & 5 \color{red}{+} (-5-2x) \\\Leftrightarrow & -15x+20& = &5-5-2x \\\Leftrightarrow & -15x \color{red}{+20} & = &0 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -15x+2x& = &0-20 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x-3)& = & 15 \color{red}{-} (-2-5x) \\\Leftrightarrow & -6x-9& = &15+2+5x \\\Leftrightarrow & -6x \color{red}{-9} & = &17 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -6x-5x& = &17+9 \\\Leftrightarrow & -11x& = &26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x-4)& = & -9 \color{red}{-} (4+x) \\\Leftrightarrow & -2x-8& = &-9-4-x \\\Leftrightarrow & -2x \color{red}{-8} & = &-13 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -2x+x& = &-13+8 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-4)& = & -10 \color{red}{-} (-11+3x) \\\Leftrightarrow & 16x-16& = &-10+11-3x \\\Leftrightarrow & 16x \color{red}{-16} & = &1 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 16x+3x& = &1+16 \\\Leftrightarrow & 19x& = &17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)