Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-3)& = & 11 \color{red}{+} (14+x) \\\Leftrightarrow & 12x-12& = &11+14+x \\\Leftrightarrow & 12x \color{red}{-12} & = &25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &25+12 \\\Leftrightarrow & 11x& = &37 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{37}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{37}{11} & & \\ & V = \left\{ \frac{37}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-4)& = & 6 \color{red}{-} (8+x) \\\Leftrightarrow & 10x-8& = &6-8-x \\\Leftrightarrow & 10x \color{red}{-8} & = &-2 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 10x+x& = &-2+8 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+1)& = & 10 \color{red}{+} (5+x) \\\Leftrightarrow & -2x+2& = &10+5+x \\\Leftrightarrow & -2x \color{red}{+2} & = &15 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -2x-x& = &15-2 \\\Leftrightarrow & -3x& = &13 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{13}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+4)& = & 4 \color{red}{-} (-12+2x) \\\Leftrightarrow & -15x+20& = &4+12-2x \\\Leftrightarrow & -15x \color{red}{+20} & = &16 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -15x+2x& = &16-20 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x+3)& = & 11 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x+18& = &11-12-5x \\\Leftrightarrow & -6x \color{red}{+18} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -6x+5x& = &-1-18 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+6)& = & -10 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x+36& = &-10-14+x \\\Leftrightarrow & 30x \color{red}{+36} & = &-24 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &-24-36 \\\Leftrightarrow & 29x& = &-60 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-60}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-60}{29} & & \\ & V = \left\{ \frac{-60}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-4)& = & -8 \color{red}{-} (4-2x) \\\Leftrightarrow & 3x-12& = &-8-4+2x \\\Leftrightarrow & 3x \color{red}{-12} & = &-12 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 3x-2x& = &-12+12 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-5)& = & -5 \color{red}{-} (-13+3x) \\\Leftrightarrow & -20x-20& = &-5+13-3x \\\Leftrightarrow & -20x \color{red}{-20} & = &8 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -20x+3x& = &8+20 \\\Leftrightarrow & -17x& = &28 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{28}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-28}{17} & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-6)& = & -13 \color{red}{+} (2+x) \\\Leftrightarrow & -20x-30& = &-13+2+x \\\Leftrightarrow & -20x \color{red}{-30} & = &-11 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -20x-x& = &-11+30 \\\Leftrightarrow & -21x& = &19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-19}{21} & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+7)& = & -3 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x+35& = &-3+4-x \\\Leftrightarrow & 30x \color{red}{+35} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &1-35 \\\Leftrightarrow & 31x& = &-34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-34}{31} & & \\ & V = \left\{ \frac{-34}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-6)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & 20x-24& = &-3-3-x \\\Leftrightarrow & 20x \color{red}{-24} & = &-6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &-6+24 \\\Leftrightarrow & 21x& = &18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-5)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x-30& = &-7+7-x \\\Leftrightarrow & 30x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &0+30 \\\Leftrightarrow & 31x& = &30 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{30}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{30}{31} & & \\ & V = \left\{ \frac{30}{31} \right\} & \\\end{align}\)