Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+2)& = & 3 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+4& = &3-4+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-1-4 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+7)& = & -1 \color{red}{+} (-14+2x) \\\Leftrightarrow & -5x+35& = &-1-14+2x \\\Leftrightarrow & -5x \color{red}{+35} & = &-15 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & -5x-2x& = &-15-35 \\\Leftrightarrow & -7x& = &-50 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-50}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{50}{7} & & \\ & V = \left\{ \frac{50}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+2)& = & 12 \color{red}{+} (7+x) \\\Leftrightarrow & -10x+10& = &12+7+x \\\Leftrightarrow & -10x \color{red}{+10} & = &19 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &19-10 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+3)& = & 3 \color{red}{+} (1+x) \\\Leftrightarrow & -12x+12& = &3+1+x \\\Leftrightarrow & -12x \color{red}{+12} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &4-12 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-4)& = & 14 \color{red}{+} (-1-2x) \\\Leftrightarrow & -15x-12& = &14-1-2x \\\Leftrightarrow & -15x \color{red}{-12} & = &13 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -15x+2x& = &13+12 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-3)& = & 13 \color{red}{-} (6+x) \\\Leftrightarrow & 10x-15& = &13-6-x \\\Leftrightarrow & 10x \color{red}{-15} & = &7 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 10x+x& = &7+15 \\\Leftrightarrow & 11x& = &22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{22}{ \color{red}{11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-1)& = & -11 \color{red}{-} (-12+x) \\\Leftrightarrow & 18x-3& = &-11+12-x \\\Leftrightarrow & 18x \color{red}{-3} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 18x+x& = &1+3 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x-1)& = & -15 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-6& = &-15+3+x \\\Leftrightarrow & 12x \color{red}{-6} & = &-12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &-12+6 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x-5)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & 4x-20& = &10-15+x \\\Leftrightarrow & 4x \color{red}{-20} & = &-5 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 4x-x& = &-5+20 \\\Leftrightarrow & 3x& = &15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{15}{ \color{red}{3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x+1)& = & -7 \color{red}{-} (7-5x) \\\Leftrightarrow & -6x+2& = &-7-7+5x \\\Leftrightarrow & -6x \color{red}{+2} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & -6x-5x& = &-14-2 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x-6)& = & 9 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x-36& = &9+10-x \\\Leftrightarrow & -30x \color{red}{-36} & = &19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -30x+x& = &19+36 \\\Leftrightarrow & -29x& = &55 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{55}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-55}{29} & & \\ & V = \left\{ \frac{-55}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+5)& = & -4 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+10& = &-4-8-x \\\Leftrightarrow & 12x \color{red}{+10} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 12x+x& = &-12-10 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)