Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x-5)& = & 11 \color{red}{+} (3-4x) \\\Leftrightarrow & -9x-15& = &11+3-4x \\\Leftrightarrow & -9x \color{red}{-15} & = &14 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -9x+4x& = &14+15 \\\Leftrightarrow & -5x& = &29 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{29}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-29}{5} & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+4)& = & 5 \color{red}{-} (3-3x) \\\Leftrightarrow & -10x+20& = &5-3+3x \\\Leftrightarrow & -10x \color{red}{+20} & = &2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -10x-3x& = &2-20 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-1)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-4& = &15+6+x \\\Leftrightarrow & 12x \color{red}{-4} & = &21 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &21+4 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-2)& = & -8 \color{red}{-} (-13+x) \\\Leftrightarrow & -6x-12& = &-8+13-x \\\Leftrightarrow & -6x \color{red}{-12} & = &5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &5+12 \\\Leftrightarrow & -5x& = &17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x-1)& = & -10 \color{red}{-} (14-5x) \\\Leftrightarrow & -36x-6& = &-10-14+5x \\\Leftrightarrow & -36x \color{red}{-6} & = &-24 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -36x-5x& = &-24+6 \\\Leftrightarrow & -41x& = &-18 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-18}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{18}{41} & & \\ & V = \left\{ \frac{18}{41} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x-5)& = & -11 \color{red}{-} (12+3x) \\\Leftrightarrow & -4x-10& = &-11-12-3x \\\Leftrightarrow & -4x \color{red}{-10} & = &-23 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -4x+3x& = &-23+10 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-3)& = & 13 \color{red}{-} (5+x) \\\Leftrightarrow & -20x-15& = &13-5-x \\\Leftrightarrow & -20x \color{red}{-15} & = &8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -20x+x& = &8+15 \\\Leftrightarrow & -19x& = &23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+6)& = & -5 \color{red}{+} (7+x) \\\Leftrightarrow & -36x+36& = &-5+7+x \\\Leftrightarrow & -36x \color{red}{+36} & = &2 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &2-36 \\\Leftrightarrow & -37x& = &-34 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-34}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{34}{37} & & \\ & V = \left\{ \frac{34}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+7)& = & -10 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+21& = &-10-14-x \\\Leftrightarrow & 12x \color{red}{+21} & = &-24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &-24-21 \\\Leftrightarrow & 13x& = &-45 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-45}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-45}{13} & & \\ & V = \left\{ \frac{-45}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+5)& = & -9 \color{red}{+} (11+x) \\\Leftrightarrow & 9x+15& = &-9+11+x \\\Leftrightarrow & 9x \color{red}{+15} & = &2 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 9x-x& = &2-15 \\\Leftrightarrow & 8x& = &-13 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-13}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-13}{8} & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-4)& = & -9 \color{red}{+} (-8-2x) \\\Leftrightarrow & 15x-12& = &-9-8-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-17 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &-17+12 \\\Leftrightarrow & 17x& = &-5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x-7)& = & 1 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x-42& = &1+15-x \\\Leftrightarrow & -24x \color{red}{-42} & = &16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &16+42 \\\Leftrightarrow & -23x& = &58 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{58}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-58}{23} & & \\ & V = \left\{ \frac{-58}{23} \right\} & \\\end{align}\)