Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+4)& = & -10 \color{red}{+} (-4+x) \\\Leftrightarrow & 15x+12& = &-10-4+x \\\Leftrightarrow & 15x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 15x-x& = &-14-12 \\\Leftrightarrow & 14x& = &-26 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-26}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+3)& = & 8 \color{red}{-} (3+x) \\\Leftrightarrow & 30x+15& = &8-3-x \\\Leftrightarrow & 30x \color{red}{+15} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &5-15 \\\Leftrightarrow & 31x& = &-10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+5)& = & 13 \color{red}{-} (10+x) \\\Leftrightarrow & 2x+10& = &13-10-x \\\Leftrightarrow & 2x \color{red}{+10} & = &3 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 2x+x& = &3-10 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x+4)& = & -6 \color{red}{-} (12+x) \\\Leftrightarrow & -18x+24& = &-6-12-x \\\Leftrightarrow & -18x \color{red}{+24} & = &-18 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -18x+x& = &-18-24 \\\Leftrightarrow & -17x& = &-42 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-42}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{42}{17} & & \\ & V = \left\{ \frac{42}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-6)& = & 9 \color{red}{+} (2+x) \\\Leftrightarrow & 6x-18& = &9+2+x \\\Leftrightarrow & 6x \color{red}{-18} & = &11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 6x-x& = &11+18 \\\Leftrightarrow & 5x& = &29 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{29}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{29}{5} & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+2)& = & 12 \color{red}{+} (-9+x) \\\Leftrightarrow & 4x+8& = &12-9+x \\\Leftrightarrow & 4x \color{red}{+8} & = &3 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &3-8 \\\Leftrightarrow & 3x& = &-5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-3)& = & -11 \color{red}{-} (-4+x) \\\Leftrightarrow & 18x-9& = &-11+4-x \\\Leftrightarrow & 18x \color{red}{-9} & = &-7 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 18x+x& = &-7+9 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+7)& = & 3 \color{red}{-} (2+x) \\\Leftrightarrow & 8x+28& = &3-2-x \\\Leftrightarrow & 8x \color{red}{+28} & = &1 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 8x+x& = &1-28 \\\Leftrightarrow & 9x& = &-27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-27}{ \color{red}{9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-6)& = & -1 \color{red}{+} (12-5x) \\\Leftrightarrow & 6x-12& = &-1+12-5x \\\Leftrightarrow & 6x \color{red}{-12} & = &11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 6x+5x& = &11+12 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+6)& = & -2 \color{red}{-} (10+x) \\\Leftrightarrow & 3x+18& = &-2-10-x \\\Leftrightarrow & 3x \color{red}{+18} & = &-12 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 3x+x& = &-12-18 \\\Leftrightarrow & 4x& = &-30 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-30}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-15}{2} & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+6)& = & 14 \color{red}{-} (14+3x) \\\Leftrightarrow & 20x+24& = &14-14-3x \\\Leftrightarrow & 20x \color{red}{+24} & = &0 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 20x+3x& = &0-24 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-5)& = & 6 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-20& = &6+4-x \\\Leftrightarrow & 12x \color{red}{-20} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &10+20 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)