Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-6)& = & 4 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x-12& = &4-2+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &2 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &2+12 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x+1)& = & 7 \color{red}{-} (-12-5x) \\\Leftrightarrow & 6x+6& = &7+12+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &19 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &19-6 \\\Leftrightarrow & x& = &13 \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-2)& = & 8 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x-6& = &8-2+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &6 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &6+6 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+5)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & 4x+10& = &-15-15+x \\\Leftrightarrow & 4x \color{red}{+10} & = &-30 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 4x-x& = &-30-10 \\\Leftrightarrow & 3x& = &-40 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-40}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-40}{3} & & \\ & V = \left\{ \frac{-40}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+3)& = & -14 \color{red}{-} (9+x) \\\Leftrightarrow & -20x+12& = &-14-9-x \\\Leftrightarrow & -20x \color{red}{+12} & = &-23 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -20x+x& = &-23-12 \\\Leftrightarrow & -19x& = &-35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-3)& = & 11 \color{red}{+} (5-3x) \\\Leftrightarrow & 4x-6& = &11+5-3x \\\Leftrightarrow & 4x \color{red}{-6} & = &16 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 4x+3x& = &16+6 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & 12 \color{red}{+} (5+x) \\\Leftrightarrow & 8x-8& = &12+5+x \\\Leftrightarrow & 8x \color{red}{-8} & = &17 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &17+8 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-4)& = & -2 \color{red}{-} (1+x) \\\Leftrightarrow & -30x-24& = &-2-1-x \\\Leftrightarrow & -30x \color{red}{-24} & = &-3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &-3+24 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-4)& = & 4 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x-24& = &4+12-x \\\Leftrightarrow & -12x \color{red}{-24} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &16+24 \\\Leftrightarrow & -11x& = &40 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{40}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-7)& = & -9 \color{red}{+} (-6-5x) \\\Leftrightarrow & 6x-14& = &-9-6-5x \\\Leftrightarrow & 6x \color{red}{-14} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & 6x+5x& = &-15+14 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-2)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & -36x-12& = &-4-12-x \\\Leftrightarrow & -36x \color{red}{-12} & = &-16 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -36x+x& = &-16+12 \\\Leftrightarrow & -35x& = &-4 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-4}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{4}{35} & & \\ & V = \left\{ \frac{4}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-2)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & -10x-10& = &-8-12+x \\\Leftrightarrow & -10x \color{red}{-10} & = &-20 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -10x-x& = &-20+10 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)