Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-1)& = & -4 \color{red}{-} (-11-5x) \\\Leftrightarrow & -6x-3& = &-4+11+5x \\\Leftrightarrow & -6x \color{red}{-3} & = &7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -6x-5x& = &7+3 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-1)& = & -12 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-4& = &-12-3+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-15+4 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-1)& = & 10 \color{red}{+} (-5-4x) \\\Leftrightarrow & -9x-3& = &10-5-4x \\\Leftrightarrow & -9x \color{red}{-3} & = &5 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & -9x+4x& = &5+3 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+5)& = & 14 \color{red}{+} (9-4x) \\\Leftrightarrow & -9x+15& = &14+9-4x \\\Leftrightarrow & -9x \color{red}{+15} & = &23 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &23 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -9x+4x& = &23-15 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-4)& = & -5 \color{red}{-} (15-5x) \\\Leftrightarrow & -18x-12& = &-5-15+5x \\\Leftrightarrow & -18x \color{red}{-12} & = &-20 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -18x-5x& = &-20+12 \\\Leftrightarrow & -23x& = &-8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x+1)& = & 7 \color{red}{+} (-5-2x) \\\Leftrightarrow & 15x+3& = &7-5-2x \\\Leftrightarrow & 15x \color{red}{+3} & = &2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 15x+2x& = &2-3 \\\Leftrightarrow & 17x& = &-1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+2)& = & 14 \color{red}{+} (4+2x) \\\Leftrightarrow & -5x+10& = &14+4+2x \\\Leftrightarrow & -5x \color{red}{+10} & = &18 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & -5x-2x& = &18-10 \\\Leftrightarrow & -7x& = &8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+6)& = & -14 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x+12& = &-14+2-x \\\Leftrightarrow & 12x \color{red}{+12} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &-12-12 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+5)& = & -10 \color{red}{-} (14-2x) \\\Leftrightarrow & -15x+15& = &-10-14+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &-24 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-24 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &-24-15 \\\Leftrightarrow & -17x& = &-39 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-39}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{39}{17} & & \\ & V = \left\{ \frac{39}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-2)& = & 9 \color{red}{+} (-3+x) \\\Leftrightarrow & 4x-8& = &9-3+x \\\Leftrightarrow & 4x \color{red}{-8} & = &6 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 4x-x& = &6+8 \\\Leftrightarrow & 3x& = &14 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{14}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x+4)& = & -4 \color{red}{+} (-11+x) \\\Leftrightarrow & 18x+24& = &-4-11+x \\\Leftrightarrow & 18x \color{red}{+24} & = &-15 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 18x-x& = &-15-24 \\\Leftrightarrow & 17x& = &-39 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-39}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-39}{17} & & \\ & V = \left\{ \frac{-39}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+1)& = & -8 \color{red}{-} (1+3x) \\\Leftrightarrow & -10x+2& = &-8-1-3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -10x+3x& = &-9-2 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)