Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x+5)& = & -4 \color{red}{+} (2+x) \\\Leftrightarrow & -24x+30& = &-4+2+x \\\Leftrightarrow & -24x \color{red}{+30} & = &-2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &-2-30 \\\Leftrightarrow & -25x& = &-32 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-32}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{32}{25} & & \\ & V = \left\{ \frac{32}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+4)& = & -10 \color{red}{-} (-12+4x) \\\Leftrightarrow & -15x+20& = &-10+12-4x \\\Leftrightarrow & -15x \color{red}{+20} & = &2 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -15x+4x& = &2-20 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+2)& = & -13 \color{red}{-} (-1+x) \\\Leftrightarrow & 8x+4& = &-13+1-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-12 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-12-4 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+3)& = & -2 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+9& = &-2+6-5x \\\Leftrightarrow & 6x \color{red}{+9} & = &4 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & 6x+5x& = &4-9 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-7)& = & 7 \color{red}{-} (-4+x) \\\Leftrightarrow & -8x-14& = &7+4-x \\\Leftrightarrow & -8x \color{red}{-14} & = &11 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -8x+x& = &11+14 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+5)& = & 3 \color{red}{-} (-9-5x) \\\Leftrightarrow & -8x+20& = &3+9+5x \\\Leftrightarrow & -8x \color{red}{+20} & = &12 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & -8x-5x& = &12-20 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-1)& = & 11 \color{red}{+} (-9-3x) \\\Leftrightarrow & 4x-4& = &11-9-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &2+4 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x-1)& = & -3 \color{red}{-} (-15+x) \\\Leftrightarrow & -30x-5& = &-3+15-x \\\Leftrightarrow & -30x \color{red}{-5} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &12+5 \\\Leftrightarrow & -29x& = &17 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{17}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-17}{29} & & \\ & V = \left\{ \frac{-17}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-6)& = & -11 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-30& = &-11-8+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-19+30 \\\Leftrightarrow & -31x& = &11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-11}{31} & & \\ & V = \left\{ \frac{-11}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-7)& = & -1 \color{red}{-} (-9-3x) \\\Leftrightarrow & 10x-35& = &-1+9+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &8 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &8+35 \\\Leftrightarrow & 7x& = &43 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{43}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{43}{7} & & \\ & V = \left\{ \frac{43}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-1)& = & 13 \color{red}{-} (11+x) \\\Leftrightarrow & 10x-2& = &13-11-x \\\Leftrightarrow & 10x \color{red}{-2} & = &2 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 10x+x& = &2+2 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x-5)& = & -14 \color{red}{-} (2+x) \\\Leftrightarrow & -15x-25& = &-14-2-x \\\Leftrightarrow & -15x \color{red}{-25} & = &-16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -15x+x& = &-16+25 \\\Leftrightarrow & -14x& = &9 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{9}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-9}{14} & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)