Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x-3)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & -24x-12& = &10-8-x \\\Leftrightarrow & -24x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &2+12 \\\Leftrightarrow & -23x& = &14 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{14}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-14}{23} & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+3)& = & -14 \color{red}{+} (5-5x) \\\Leftrightarrow & -16x+12& = &-14+5-5x \\\Leftrightarrow & -16x \color{red}{+12} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -16x+5x& = &-9-12 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+6)& = & 9 \color{red}{+} (5+3x) \\\Leftrightarrow & 16x+24& = &9+5+3x \\\Leftrightarrow & 16x \color{red}{+24} & = &14 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 16x-3x& = &14-24 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-2x+7)& = & -11 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+42& = &-11+5-x \\\Leftrightarrow & -12x \color{red}{+42} & = &-6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &-6-42 \\\Leftrightarrow & -11x& = &-48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{48}{11} & & \\ & V = \left\{ \frac{48}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-2)& = & -13 \color{red}{+} (4+x) \\\Leftrightarrow & -4x-8& = &-13+4+x \\\Leftrightarrow & -4x \color{red}{-8} & = &-9 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &-9+8 \\\Leftrightarrow & -5x& = &-1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-1)& = & -10 \color{red}{-} (-7-5x) \\\Leftrightarrow & -3x-3& = &-10+7+5x \\\Leftrightarrow & -3x \color{red}{-3} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -3x-5x& = &-3+3 \\\Leftrightarrow & -8x& = &0 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{0}{ \color{red}{-8} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x+2)& = & -6 \color{red}{+} (1+x) \\\Leftrightarrow & 18x+12& = &-6+1+x \\\Leftrightarrow & 18x \color{red}{+12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &-5-12 \\\Leftrightarrow & 17x& = &-17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-17}{ \color{red}{17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-1)& = & 4 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x-2& = &4+6+5x \\\Leftrightarrow & -8x \color{red}{-2} & = &10 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & -8x-5x& = &10+2 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-3)& = & 12 \color{red}{+} (8+x) \\\Leftrightarrow & -20x-15& = &12+8+x \\\Leftrightarrow & -20x \color{red}{-15} & = &20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &20+15 \\\Leftrightarrow & -21x& = &35 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{35}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x-6)& = & -11 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-36& = &-11+14-x \\\Leftrightarrow & 12x \color{red}{-36} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 12x+x& = &3+36 \\\Leftrightarrow & 13x& = &39 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{39}{ \color{red}{13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-1)& = & -8 \color{red}{-} (-4-5x) \\\Leftrightarrow & 6x-6& = &-8+4+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-4+6 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+7)& = & 10 \color{red}{-} (-2-2x) \\\Leftrightarrow & 9x+21& = &10+2+2x \\\Leftrightarrow & 9x \color{red}{+21} & = &12 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 9x-2x& = &12-21 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)