Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-2)& = & 4 \color{red}{+} (1+x) \\\Leftrightarrow & -18x-12& = &4+1+x \\\Leftrightarrow & -18x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &5+12 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-4)& = & 8 \color{red}{+} (11-3x) \\\Leftrightarrow & 10x-8& = &8+11-3x \\\Leftrightarrow & 10x \color{red}{-8} & = &19 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 10x+3x& = &19+8 \\\Leftrightarrow & 13x& = &27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+2)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & 6x+4& = &-14+8+x \\\Leftrightarrow & 6x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 6x-x& = &-6-4 \\\Leftrightarrow & 5x& = &-10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-10}{ \color{red}{5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-6)& = & 2 \color{red}{-} (8+x) \\\Leftrightarrow & 30x-36& = &2-8-x \\\Leftrightarrow & 30x \color{red}{-36} & = &-6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &-6+36 \\\Leftrightarrow & 31x& = &30 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{30}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{30}{31} & & \\ & V = \left\{ \frac{30}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+4)& = & 14 \color{red}{+} (6+x) \\\Leftrightarrow & 20x+16& = &14+6+x \\\Leftrightarrow & 20x \color{red}{+16} & = &20 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &20-16 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x+1)& = & -9 \color{red}{+} (-14+x) \\\Leftrightarrow & -36x+6& = &-9-14+x \\\Leftrightarrow & -36x \color{red}{+6} & = &-23 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -36x-x& = &-23-6 \\\Leftrightarrow & -37x& = &-29 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-29}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{29}{37} & & \\ & V = \left\{ \frac{29}{37} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+4)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & 30x+24& = &14-12-x \\\Leftrightarrow & 30x \color{red}{+24} & = &2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 30x+x& = &2-24 \\\Leftrightarrow & 31x& = &-22 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-22}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-22}{31} & & \\ & V = \left\{ \frac{-22}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+4)& = & -1 \color{red}{+} (-13+x) \\\Leftrightarrow & 24x+24& = &-1-13+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-14-24 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-6)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-24& = &-10-12-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-22+24 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-3)& = & 3 \color{red}{+} (-7-5x) \\\Leftrightarrow & 18x-9& = &3-7-5x \\\Leftrightarrow & 18x \color{red}{-9} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 18x+5x& = &-4+9 \\\Leftrightarrow & 23x& = &5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+2)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & 6x+6& = &14-7+x \\\Leftrightarrow & 6x \color{red}{+6} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &7-6 \\\Leftrightarrow & 5x& = &1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+6)& = & 9 \color{red}{-} (15-2x) \\\Leftrightarrow & 15x+30& = &9-15+2x \\\Leftrightarrow & 15x \color{red}{+30} & = &-6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 15x-2x& = &-6-30 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)