Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x-1)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & -20x-4& = &2+3+x \\\Leftrightarrow & -20x \color{red}{-4} & = &5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -20x-x& = &5+4 \\\Leftrightarrow & -21x& = &9 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{9}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x-4)& = & -7 \color{red}{+} (-10-2x) \\\Leftrightarrow & -15x-12& = &-7-10-2x \\\Leftrightarrow & -15x \color{red}{-12} & = &-17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -15x+2x& = &-17+12 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-6)& = & -5 \color{red}{-} (7+x) \\\Leftrightarrow & 4x-24& = &-5-7-x \\\Leftrightarrow & 4x \color{red}{-24} & = &-12 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 4x+x& = &-12+24 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-2)& = & -7 \color{red}{+} (3+x) \\\Leftrightarrow & 9x-6& = &-7+3+x \\\Leftrightarrow & 9x \color{red}{-6} & = &-4 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 9x-x& = &-4+6 \\\Leftrightarrow & 8x& = &2 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{2}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-3)& = & 11 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x-18& = &11-15-5x \\\Leftrightarrow & -6x \color{red}{-18} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -6x+5x& = &-4+18 \\\Leftrightarrow & -x& = &14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{14}{ \color{red}{-1} } \\\Leftrightarrow & x = -14 & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x+4)& = & -9 \color{red}{+} (-6-5x) \\\Leftrightarrow & 18x+12& = &-9-6-5x \\\Leftrightarrow & 18x \color{red}{+12} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 18x+5x& = &-15-12 \\\Leftrightarrow & 23x& = &-27 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-27}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-6)& = & -8 \color{red}{-} (2-4x) \\\Leftrightarrow & -5x-30& = &-8-2+4x \\\Leftrightarrow & -5x \color{red}{-30} & = &-10 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -5x-4x& = &-10+30 \\\Leftrightarrow & -9x& = &20 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{20}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-20}{9} & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+6)& = & -5 \color{red}{-} (-5-2x) \\\Leftrightarrow & 15x+30& = &-5+5+2x \\\Leftrightarrow & 15x \color{red}{+30} & = &0 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 15x-2x& = &0-30 \\\Leftrightarrow & 13x& = &-30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+7)& = & 7 \color{red}{-} (7-5x) \\\Leftrightarrow & -18x+21& = &7-7+5x \\\Leftrightarrow & -18x \color{red}{+21} & = &0 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -18x-5x& = &0-21 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+7)& = & -13 \color{red}{+} (-13-2x) \\\Leftrightarrow & 15x+21& = &-13-13-2x \\\Leftrightarrow & 15x \color{red}{+21} & = &-26 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &-26 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 15x+2x& = &-26-21 \\\Leftrightarrow & 17x& = &-47 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-47}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-47}{17} & & \\ & V = \left\{ \frac{-47}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+7)& = & -10 \color{red}{+} (2-3x) \\\Leftrightarrow & 4x+14& = &-10+2-3x \\\Leftrightarrow & 4x \color{red}{+14} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 4x+3x& = &-8-14 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+3)& = & 13 \color{red}{-} (4-5x) \\\Leftrightarrow & 6x+9& = &13-4+5x \\\Leftrightarrow & 6x \color{red}{+9} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 6x-5x& = &9-9 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)