Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x+6)& = & -4 \color{red}{-} (8+x) \\\Leftrightarrow & 36x+36& = &-4-8-x \\\Leftrightarrow & 36x \color{red}{+36} & = &-12 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 36x+x& = &-12-36 \\\Leftrightarrow & 37x& = &-48 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-48}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-48}{37} & & \\ & V = \left\{ \frac{-48}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x-3)& = & 9 \color{red}{-} (6+x) \\\Leftrightarrow & 8x-6& = &9-6-x \\\Leftrightarrow & 8x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 8x+x& = &3+6 \\\Leftrightarrow & 9x& = &9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{9}{ \color{red}{9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-3)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-12& = &10+13-x \\\Leftrightarrow & -12x \color{red}{-12} & = &23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &23+12 \\\Leftrightarrow & -11x& = &35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+1)& = & 4 \color{red}{-} (-10-4x) \\\Leftrightarrow & -9x+3& = &4+10+4x \\\Leftrightarrow & -9x \color{red}{+3} & = &14 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & -9x-4x& = &14-3 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x-5)& = & 4 \color{red}{+} (-2+3x) \\\Leftrightarrow & -20x-20& = &4-2+3x \\\Leftrightarrow & -20x \color{red}{-20} & = &2 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -20x-3x& = &2+20 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+7)& = & 11 \color{red}{+} (10-2x) \\\Leftrightarrow & -9x+21& = &11+10-2x \\\Leftrightarrow & -9x \color{red}{+21} & = &21 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -9x+2x& = &21-21 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-7)& = & 5 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-42& = &5-14-x \\\Leftrightarrow & -12x \color{red}{-42} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &-9+42 \\\Leftrightarrow & -11x& = &33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{33}{ \color{red}{-11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+5)& = & -11 \color{red}{-} (5+4x) \\\Leftrightarrow & 3x+15& = &-11-5-4x \\\Leftrightarrow & 3x \color{red}{+15} & = &-16 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 3x+4x& = &-16-15 \\\Leftrightarrow & 7x& = &-31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+1)& = & 2 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+6& = &2-8+x \\\Leftrightarrow & -24x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -24x-x& = &-6-6 \\\Leftrightarrow & -25x& = &-12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{12}{25} & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+1)& = & -4 \color{red}{-} (7+4x) \\\Leftrightarrow & 15x+5& = &-4-7-4x \\\Leftrightarrow & 15x \color{red}{+5} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 15x+4x& = &-11-5 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+3)& = & -14 \color{red}{+} (-3-3x) \\\Leftrightarrow & 4x+6& = &-14-3-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &-17-6 \\\Leftrightarrow & 7x& = &-23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-2)& = & 6 \color{red}{+} (15+x) \\\Leftrightarrow & -24x-8& = &6+15+x \\\Leftrightarrow & -24x \color{red}{-8} & = &21 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &21+8 \\\Leftrightarrow & -25x& = &29 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{29}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-29}{25} & & \\ & V = \left\{ \frac{-29}{25} \right\} & \\\end{align}\)