Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-7)& = & 15 \color{red}{-} (5+x) \\\Leftrightarrow & 20x-35& = &15-5-x \\\Leftrightarrow & 20x \color{red}{-35} & = &10 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 20x+x& = &10+35 \\\Leftrightarrow & 21x& = &45 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{45}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+7)& = & -4 \color{red}{+} (3-4x) \\\Leftrightarrow & -9x+21& = &-4+3-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &-1-21 \\\Leftrightarrow & -5x& = &-22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{22}{5} & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+6)& = & -12 \color{red}{+} (14-5x) \\\Leftrightarrow & 18x+18& = &-12+14-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &2-18 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+6)& = & -12 \color{red}{+} (8+x) \\\Leftrightarrow & 12x+24& = &-12+8+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-4-24 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x-5)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & 2x-10& = &11-10-x \\\Leftrightarrow & 2x \color{red}{-10} & = &1 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &1+10 \\\Leftrightarrow & 3x& = &11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x-6)& = & 12 \color{red}{-} (11+3x) \\\Leftrightarrow & -10x-12& = &12-11-3x \\\Leftrightarrow & -10x \color{red}{-12} & = &1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -10x+3x& = &1+12 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-1)& = & 15 \color{red}{-} (-3+x) \\\Leftrightarrow & -4x-2& = &15+3-x \\\Leftrightarrow & -4x \color{red}{-2} & = &18 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -4x+x& = &18+2 \\\Leftrightarrow & -3x& = &20 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{20}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-4)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & 24x-24& = &-11-7-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-18 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-18+24 \\\Leftrightarrow & 25x& = &6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+2)& = & 2 \color{red}{-} (-14+x) \\\Leftrightarrow & 36x+12& = &2+14-x \\\Leftrightarrow & 36x \color{red}{+12} & = &16 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 36x+x& = &16-12 \\\Leftrightarrow & 37x& = &4 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{4}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{4}{37} & & \\ & V = \left\{ \frac{4}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+7)& = & 8 \color{red}{+} (-13+x) \\\Leftrightarrow & 2x+14& = &8-13+x \\\Leftrightarrow & 2x \color{red}{+14} & = &-5 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &-5-14 \\\Leftrightarrow & x& = &-19 \\ & V = \left\{ -19 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+2)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & -30x+12& = &15-14-x \\\Leftrightarrow & -30x \color{red}{+12} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &1-12 \\\Leftrightarrow & -29x& = &-11 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-11}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{11}{29} & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-1)& = & 6 \color{red}{+} (-8-3x) \\\Leftrightarrow & 10x-5& = &6-8-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &-2+5 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)