Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-4)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & 12x-16& = &2+11+x \\\Leftrightarrow & 12x \color{red}{-16} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &13+16 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-2)& = & -6 \color{red}{+} (4-3x) \\\Leftrightarrow & -25x-10& = &-6+4-3x \\\Leftrightarrow & -25x \color{red}{-10} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -25x+3x& = &-2+10 \\\Leftrightarrow & -22x& = &8 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{8}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-1)& = & -6 \color{red}{-} (-11-5x) \\\Leftrightarrow & 18x-3& = &-6+11+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &5+3 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-4)& = & -3 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-12& = &-3+15+x \\\Leftrightarrow & -12x \color{red}{-12} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &12+12 \\\Leftrightarrow & -13x& = &24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x+6)& = & -15 \color{red}{+} (-8-5x) \\\Leftrightarrow & 8x+12& = &-15-8-5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-23 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 8x+5x& = &-23-12 \\\Leftrightarrow & 13x& = &-35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-35}{13} & & \\ & V = \left\{ \frac{-35}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-1)& = & 10 \color{red}{+} (11-2x) \\\Leftrightarrow & 15x-5& = &10+11-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &21 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &21+5 \\\Leftrightarrow & 17x& = &26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{26}{17} & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x-6)& = & -13 \color{red}{+} (14+x) \\\Leftrightarrow & 12x-36& = &-13+14+x \\\Leftrightarrow & 12x \color{red}{-36} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 12x-x& = &1+36 \\\Leftrightarrow & 11x& = &37 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{37}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{37}{11} & & \\ & V = \left\{ \frac{37}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+2)& = & 10 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+4& = &10-15-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-5-4 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-3)& = & -1 \color{red}{+} (-9-4x) \\\Leftrightarrow & 9x-9& = &-1-9-4x \\\Leftrightarrow & 9x \color{red}{-9} & = &-10 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 9x+4x& = &-10+9 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-4)& = & 13 \color{red}{-} (11+x) \\\Leftrightarrow & 6x-24& = &13-11-x \\\Leftrightarrow & 6x \color{red}{-24} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &2+24 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-3)& = & 11 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x-15& = &11+4-x \\\Leftrightarrow & -20x \color{red}{-15} & = &15 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -20x+x& = &15+15 \\\Leftrightarrow & -19x& = &30 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{30}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-30}{19} & & \\ & V = \left\{ \frac{-30}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+1)& = & 6 \color{red}{-} (2+x) \\\Leftrightarrow & 18x+6& = &6-2-x \\\Leftrightarrow & 18x \color{red}{+6} & = &4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &4-6 \\\Leftrightarrow & 19x& = &-2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)