Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x-3)& = & 15 \color{red}{+} (4-3x) \\\Leftrightarrow & -4x-12& = &15+4-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &19+12 \\\Leftrightarrow & -x& = &31 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{31}{ \color{red}{-1} } \\\Leftrightarrow & x = -31 & & \\ & V = \left\{ -31 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-5)& = & -8 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x-30& = &-8+10-x \\\Leftrightarrow & 12x \color{red}{-30} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 12x+x& = &2+30 \\\Leftrightarrow & 13x& = &32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-7)& = & -15 \color{red}{+} (9-5x) \\\Leftrightarrow & 18x-42& = &-15+9-5x \\\Leftrightarrow & 18x \color{red}{-42} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 18x+5x& = &-6+42 \\\Leftrightarrow & 23x& = &36 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{36}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{36}{23} & & \\ & V = \left\{ \frac{36}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-2)& = & 8 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-4& = &8+13-x \\\Leftrightarrow & -12x \color{red}{-4} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &21+4 \\\Leftrightarrow & -11x& = &25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-7)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & -5x-35& = &11+3+x \\\Leftrightarrow & -5x \color{red}{-35} & = &14 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -5x-x& = &14+35 \\\Leftrightarrow & -6x& = &49 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{49}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-49}{6} & & \\ & V = \left\{ \frac{-49}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-1)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & -9x-3& = &-14+8+x \\\Leftrightarrow & -9x \color{red}{-3} & = &-6 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -9x-x& = &-6+3 \\\Leftrightarrow & -10x& = &-3 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-3}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x+2)& = & 2 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+8& = &2+7-x \\\Leftrightarrow & 12x \color{red}{+8} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &9-8 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+4)& = & 11 \color{red}{+} (-7+3x) \\\Leftrightarrow & -8x+8& = &11-7+3x \\\Leftrightarrow & -8x \color{red}{+8} & = &4 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -8x-3x& = &4-8 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-3)& = & 1 \color{red}{-} (6-2x) \\\Leftrightarrow & 5x-15& = &1-6+2x \\\Leftrightarrow & 5x \color{red}{-15} & = &-5 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 5x-2x& = &-5+15 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+5)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & 8x+20& = &-15+4+x \\\Leftrightarrow & 8x \color{red}{+20} & = &-11 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 8x-x& = &-11-20 \\\Leftrightarrow & 7x& = &-31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-5)& = & -14 \color{red}{-} (-13+x) \\\Leftrightarrow & 30x-25& = &-14+13-x \\\Leftrightarrow & 30x \color{red}{-25} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &-1+25 \\\Leftrightarrow & 31x& = &24 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{24}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x-5)& = & 5 \color{red}{+} (-8+x) \\\Leftrightarrow & 3x-15& = &5-8+x \\\Leftrightarrow & 3x \color{red}{-15} & = &-3 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 3x-x& = &-3+15 \\\Leftrightarrow & 2x& = &12 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{12}{ \color{red}{2} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)