Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-7)& = & -3 \color{red}{-} (-8-5x) \\\Leftrightarrow & -36x-42& = &-3+8+5x \\\Leftrightarrow & -36x \color{red}{-42} & = &5 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -36x-5x& = &5+42 \\\Leftrightarrow & -41x& = &47 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{47}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-47}{41} & & \\ & V = \left\{ \frac{-47}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x-7)& = & -4 \color{red}{+} (6-5x) \\\Leftrightarrow & -8x-14& = &-4+6-5x \\\Leftrightarrow & -8x \color{red}{-14} & = &2 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & -8x+5x& = &2+14 \\\Leftrightarrow & -3x& = &16 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{16}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-16}{3} & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-4)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x-16& = &-7+7-x \\\Leftrightarrow & -24x \color{red}{-16} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &0+16 \\\Leftrightarrow & -23x& = &16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+5)& = & -15 \color{red}{-} (-1+3x) \\\Leftrightarrow & 4x+10& = &-15+1-3x \\\Leftrightarrow & 4x \color{red}{+10} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 4x+3x& = &-14-10 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+3)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & 2x+6& = &-3-13-x \\\Leftrightarrow & 2x \color{red}{+6} & = &-16 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &-16-6 \\\Leftrightarrow & 3x& = &-22 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-22}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-22}{3} & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x-6)& = & 8 \color{red}{-} (-10-3x) \\\Leftrightarrow & -4x-24& = &8+10+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &18 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &18+24 \\\Leftrightarrow & -7x& = &42 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{42}{ \color{red}{-7} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-3)& = & -5 \color{red}{+} (-12+3x) \\\Leftrightarrow & 10x-15& = &-5-12+3x \\\Leftrightarrow & 10x \color{red}{-15} & = &-17 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & 10x-3x& = &-17+15 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-3)& = & -13 \color{red}{-} (4+x) \\\Leftrightarrow & -12x-18& = &-13-4-x \\\Leftrightarrow & -12x \color{red}{-18} & = &-17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &-17+18 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+3)& = & -14 \color{red}{-} (4-5x) \\\Leftrightarrow & 3x+9& = &-14-4+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &-18-9 \\\Leftrightarrow & -2x& = &-27 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-27}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{27}{2} & & \\ & V = \left\{ \frac{27}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x-6)& = & 7 \color{red}{-} (15+x) \\\Leftrightarrow & -18x-18& = &7-15-x \\\Leftrightarrow & -18x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -18x+x& = &-8+18 \\\Leftrightarrow & -17x& = &10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+5)& = & -15 \color{red}{+} (14+x) \\\Leftrightarrow & -15x+15& = &-15+14+x \\\Leftrightarrow & -15x \color{red}{+15} & = &-1 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -15x-x& = &-1-15 \\\Leftrightarrow & -16x& = &-16 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-16}{ \color{red}{-16} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-1)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-2& = &11+3+x \\\Leftrightarrow & 12x \color{red}{-2} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &14+2 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)