Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(x+3)=3+(3+x)\)
2. \(2(3x+4)=14-(12+x)\)
3. \(5(-x+4)=-7+(-4-2x)\)
4. \(4(5x+5)=10+(-14+x)\)
5. \(3(6x-1)=-5-(14-5x)\)
6. \(3(-3x+7)=8-(-4+2x)\)
7. \(6(5x-2)=-11-(-12+29x)\)
8. \(4(-2x+6)=2+(8+3x)\)
9. \(3(x+5)=6-(11+x)\)
10. \(6(3x-5)=2-(3+x)\)
11. \(6(-3x-2)=11-(10+x)\)
12. \(5(4x+5)=-9-(1+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+3)& = & 3 \color{red}{+} (3+x) \\\Leftrightarrow & 2x+6& = &3+3+x \\\Leftrightarrow & 2x \color{red}{+6} & = &6 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 2x-x& = &6-6 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+4)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & 6x+8& = &14-12-x \\\Leftrightarrow & 6x \color{red}{+8} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 6x+x& = &2-8 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x+4)& = & -7 \color{red}{+} (-4-2x) \\\Leftrightarrow & -5x+20& = &-7-4-2x \\\Leftrightarrow & -5x \color{red}{+20} & = &-11 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -5x+2x& = &-11-20 \\\Leftrightarrow & -3x& = &-31 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-31}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{31}{3} & & \\ & V = \left\{ \frac{31}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+5)& = & 10 \color{red}{+} (-14+x) \\\Leftrightarrow & 20x+20& = &10-14+x \\\Leftrightarrow & 20x \color{red}{+20} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &-4-20 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-1)& = & -5 \color{red}{-} (14-5x) \\\Leftrightarrow & 18x-3& = &-5-14+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-19 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &-19+3 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+7)& = & 8 \color{red}{-} (-4+2x) \\\Leftrightarrow & -9x+21& = &8+4-2x \\\Leftrightarrow & -9x \color{red}{+21} & = &12 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -9x+2x& = &12-21 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-2)& = & -11 \color{red}{-} (-12+29x) \\\Leftrightarrow & 30x-12& = &-11+12-29x \\\Leftrightarrow & 30x \color{red}{-12} & = &1 \color{red}{-29x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+29x} & = &1 \color{red}{-29x} \color{blue}{+29x} \color{blue}{+12} \\\Leftrightarrow & 30x+29x& = &1+12 \\\Leftrightarrow & 59x& = &13 \\\Leftrightarrow & \frac{59x}{ \color{red}{59} }& = &\frac{13}{ \color{red}{59} } \\\Leftrightarrow & x = \frac{13}{59} & & \\ & V = \left\{ \frac{13}{59} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x+6)& = & 2 \color{red}{+} (8+3x) \\\Leftrightarrow & -8x+24& = &2+8+3x \\\Leftrightarrow & -8x \color{red}{+24} & = &10 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -8x-3x& = &10-24 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+5)& = & 6 \color{red}{-} (11+x) \\\Leftrightarrow & 3x+15& = &6-11-x \\\Leftrightarrow & 3x \color{red}{+15} & = &-5 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 3x+x& = &-5-15 \\\Leftrightarrow & 4x& = &-20 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-20}{ \color{red}{4} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x-5)& = & 2 \color{red}{-} (3+x) \\\Leftrightarrow & 18x-30& = &2-3-x \\\Leftrightarrow & 18x \color{red}{-30} & = &-1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 18x+x& = &-1+30 \\\Leftrightarrow & 19x& = &29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x-2)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & -18x-12& = &11-10-x \\\Leftrightarrow & -18x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &1+12 \\\Leftrightarrow & -17x& = &13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+5)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & 20x+25& = &-9-1-x \\\Leftrightarrow & 20x \color{red}{+25} & = &-10 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 20x+x& = &-10-25 \\\Leftrightarrow & 21x& = &-35 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-35}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)