Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+1)& = & 11 \color{red}{-} (14+x) \\\Leftrightarrow & -6x+3& = &11-14-x \\\Leftrightarrow & -6x \color{red}{+3} & = &-3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -6x+x& = &-3-3 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+5)& = & 15 \color{red}{-} (10+x) \\\Leftrightarrow & 20x+25& = &15-10-x \\\Leftrightarrow & 20x \color{red}{+25} & = &5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 20x+x& = &5-25 \\\Leftrightarrow & 21x& = &-20 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-20}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-20}{21} & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-1)& = & -8 \color{red}{+} (-9+x) \\\Leftrightarrow & -20x-4& = &-8-9+x \\\Leftrightarrow & -20x \color{red}{-4} & = &-17 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -20x-x& = &-17+4 \\\Leftrightarrow & -21x& = &-13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+1)& = & 7 \color{red}{+} (9+x) \\\Leftrightarrow & 4x+4& = &7+9+x \\\Leftrightarrow & 4x \color{red}{+4} & = &16 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &16-4 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-2)& = & 4 \color{red}{+} (7+2x) \\\Leftrightarrow & 15x-6& = &4+7+2x \\\Leftrightarrow & 15x \color{red}{-6} & = &11 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & 15x-2x& = &11+6 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+3)& = & -12 \color{red}{+} (-1-5x) \\\Leftrightarrow & 8x+12& = &-12-1-5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-13 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 8x+5x& = &-13-12 \\\Leftrightarrow & 13x& = &-25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x-2)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & 24x-12& = &2+11+x \\\Leftrightarrow & 24x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &13+12 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+3)& = & -14 \color{red}{-} (14+x) \\\Leftrightarrow & 6x+9& = &-14-14-x \\\Leftrightarrow & 6x \color{red}{+9} & = &-28 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 6x+x& = &-28-9 \\\Leftrightarrow & 7x& = &-37 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-37}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-37}{7} & & \\ & V = \left\{ \frac{-37}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+1)& = & -12 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x+4& = &-12-1+x \\\Leftrightarrow & 20x \color{red}{+4} & = &-13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 20x-x& = &-13-4 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-1)& = & 3 \color{red}{+} (-14-2x) \\\Leftrightarrow & -5x-5& = &3-14-2x \\\Leftrightarrow & -5x \color{red}{-5} & = &-11 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & -5x+2x& = &-11+5 \\\Leftrightarrow & -3x& = &-6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-6}{ \color{red}{-3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+3)& = & -15 \color{red}{+} (-5+4x) \\\Leftrightarrow & 15x+9& = &-15-5+4x \\\Leftrightarrow & 15x \color{red}{+9} & = &-20 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &-20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 15x-4x& = &-20-9 \\\Leftrightarrow & 11x& = &-29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+1)& = & -7 \color{red}{+} (-14+x) \\\Leftrightarrow & -10x+5& = &-7-14+x \\\Leftrightarrow & -10x \color{red}{+5} & = &-21 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -10x-x& = &-21-5 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)