Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x-6)& = & -5 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-18& = &-5+6+x \\\Leftrightarrow & 12x \color{red}{-18} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &1+18 \\\Leftrightarrow & 11x& = &19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-2)& = & -6 \color{red}{+} (-9+x) \\\Leftrightarrow & 3x-6& = &-6-9+x \\\Leftrightarrow & 3x \color{red}{-6} & = &-15 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 3x-x& = &-15+6 \\\Leftrightarrow & 2x& = &-9 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-9}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-9}{2} & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+6)& = & -7 \color{red}{-} (-13+x) \\\Leftrightarrow & 18x+18& = &-7+13-x \\\Leftrightarrow & 18x \color{red}{+18} & = &6 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 18x+x& = &6-18 \\\Leftrightarrow & 19x& = &-12 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-12}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x-2)& = & -13 \color{red}{-} (11+x) \\\Leftrightarrow & 10x-10& = &-13-11-x \\\Leftrightarrow & 10x \color{red}{-10} & = &-24 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 10x+x& = &-24+10 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+5)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -36x+30& = &-7-8+x \\\Leftrightarrow & -36x \color{red}{+30} & = &-15 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -36x-x& = &-15-30 \\\Leftrightarrow & -37x& = &-45 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-45}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{45}{37} & & \\ & V = \left\{ \frac{45}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+5)& = & -7 \color{red}{+} (2+x) \\\Leftrightarrow & -12x+10& = &-7+2+x \\\Leftrightarrow & -12x \color{red}{+10} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -12x-x& = &-5-10 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x+2)& = & -1 \color{red}{+} (-15+3x) \\\Leftrightarrow & 16x+8& = &-1-15+3x \\\Leftrightarrow & 16x \color{red}{+8} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 16x-3x& = &-16-8 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+4)& = & -10 \color{red}{-} (12-5x) \\\Leftrightarrow & 16x+16& = &-10-12+5x \\\Leftrightarrow & 16x \color{red}{+16} & = &-22 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & 16x-5x& = &-22-16 \\\Leftrightarrow & 11x& = &-38 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-38}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+3)& = & -6 \color{red}{-} (2-3x) \\\Leftrightarrow & -4x+6& = &-6-2+3x \\\Leftrightarrow & -4x \color{red}{+6} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -4x-3x& = &-8-6 \\\Leftrightarrow & -7x& = &-14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-14}{ \color{red}{-7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-7)& = & 9 \color{red}{-} (10-3x) \\\Leftrightarrow & 10x-35& = &9-10+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &-1+35 \\\Leftrightarrow & 7x& = &34 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{34}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{34}{7} & & \\ & V = \left\{ \frac{34}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-6)& = & -4 \color{red}{-} (-10+4x) \\\Leftrightarrow & -9x-18& = &-4+10-4x \\\Leftrightarrow & -9x \color{red}{-18} & = &6 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & -9x+4x& = &6+18 \\\Leftrightarrow & -5x& = &24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-6)& = & 11 \color{red}{-} (-12-3x) \\\Leftrightarrow & 10x-30& = &11+12+3x \\\Leftrightarrow & 10x \color{red}{-30} & = &23 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &23 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 10x-3x& = &23+30 \\\Leftrightarrow & 7x& = &53 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{53}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{53}{7} & & \\ & V = \left\{ \frac{53}{7} \right\} & \\\end{align}\)