Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-4x+3)& = & -11 \color{red}{-} (-12+3x) \\\Leftrightarrow & -16x+12& = &-11+12-3x \\\Leftrightarrow & -16x \color{red}{+12} & = &1 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -16x+3x& = &1-12 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-2)& = & 11 \color{red}{-} (-7+3x) \\\Leftrightarrow & 8x-8& = &11+7-3x \\\Leftrightarrow & 8x \color{red}{-8} & = &18 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 8x+3x& = &18+8 \\\Leftrightarrow & 11x& = &26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+6)& = & -4 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x+36& = &-4-15+x \\\Leftrightarrow & 30x \color{red}{+36} & = &-19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &-19-36 \\\Leftrightarrow & 29x& = &-55 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-55}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-55}{29} & & \\ & V = \left\{ \frac{-55}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-3)& = & -7 \color{red}{-} (10+x) \\\Leftrightarrow & -12x-6& = &-7-10-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-17+6 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+5)& = & -3 \color{red}{+} (5+x) \\\Leftrightarrow & 36x+30& = &-3+5+x \\\Leftrightarrow & 36x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 36x-x& = &2-30 \\\Leftrightarrow & 35x& = &-28 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-28}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-4)& = & 10 \color{red}{-} (7+4x) \\\Leftrightarrow & 9x-12& = &10-7-4x \\\Leftrightarrow & 9x \color{red}{-12} & = &3 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & 9x+4x& = &3+12 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-3)& = & -13 \color{red}{-} (11+3x) \\\Leftrightarrow & 2x-6& = &-13-11-3x \\\Leftrightarrow & 2x \color{red}{-6} & = &-24 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 2x+3x& = &-24+6 \\\Leftrightarrow & 5x& = &-18 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-18}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-18}{5} & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x+4)& = & -6 \color{red}{-} (-11+3x) \\\Leftrightarrow & -4x+8& = &-6+11-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &5 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &5-8 \\\Leftrightarrow & -x& = &-3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-3}{ \color{red}{-1} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x-1)& = & 12 \color{red}{-} (11-2x) \\\Leftrightarrow & 15x-3& = &12-11+2x \\\Leftrightarrow & 15x \color{red}{-3} & = &1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 15x-2x& = &1+3 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+6)& = & -3 \color{red}{-} (-2+x) \\\Leftrightarrow & -36x+36& = &-3+2-x \\\Leftrightarrow & -36x \color{red}{+36} & = &-1 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -36x+x& = &-1-36 \\\Leftrightarrow & -35x& = &-37 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-37}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{37}{35} & & \\ & V = \left\{ \frac{37}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-7)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & -6x-14& = &-6+13+x \\\Leftrightarrow & -6x \color{red}{-14} & = &7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -6x-x& = &7+14 \\\Leftrightarrow & -7x& = &21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{21}{ \color{red}{-7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-5)& = & 9 \color{red}{+} (-6-5x) \\\Leftrightarrow & 6x-30& = &9-6-5x \\\Leftrightarrow & 6x \color{red}{-30} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 6x+5x& = &3+30 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)