Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x-1)& = & 8 \color{red}{-} (-13-4x) \\\Leftrightarrow & 9x-3& = &8+13+4x \\\Leftrightarrow & 9x \color{red}{-3} & = &21 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 9x-4x& = &21+3 \\\Leftrightarrow & 5x& = &24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x-2)& = & -14 \color{red}{-} (5+3x) \\\Leftrightarrow & 4x-8& = &-14-5-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-19+8 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-4)& = & -1 \color{red}{+} (9-3x) \\\Leftrightarrow & 4x-8& = &-1+9-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &8 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &8+8 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x-3)& = & 3 \color{red}{+} (13-3x) \\\Leftrightarrow & -10x-6& = &3+13-3x \\\Leftrightarrow & -10x \color{red}{-6} & = &16 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -10x+3x& = &16+6 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+4)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & -3x+12& = &3-9-x \\\Leftrightarrow & -3x \color{red}{+12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -3x+x& = &-6-12 \\\Leftrightarrow & -2x& = &-18 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-18}{ \color{red}{-2} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-1)& = & -3 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x-2& = &-3+15+5x \\\Leftrightarrow & 6x \color{red}{-2} & = &12 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 6x-5x& = &12+2 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+1)& = & -3 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+6& = &-3-14+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-17-6 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-4)& = & 2 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x-12& = &2-12+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-10+12 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-3)& = & -6 \color{red}{+} (-10+x) \\\Leftrightarrow & -24x-18& = &-6-10+x \\\Leftrightarrow & -24x \color{red}{-18} & = &-16 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &-16+18 \\\Leftrightarrow & -25x& = &2 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{2}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-7)& = & -3 \color{red}{-} (-13-3x) \\\Leftrightarrow & -4x-28& = &-3+13+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &10 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &10+28 \\\Leftrightarrow & -7x& = &38 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{38}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-38}{7} & & \\ & V = \left\{ \frac{-38}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x-6)& = & 6 \color{red}{+} (-1+x) \\\Leftrightarrow & -8x-24& = &6-1+x \\\Leftrightarrow & -8x \color{red}{-24} & = &5 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -8x-x& = &5+24 \\\Leftrightarrow & -9x& = &29 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{29}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-29}{9} & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+5)& = & -7 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+15& = &-7+10-x \\\Leftrightarrow & -12x \color{red}{+15} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &3-15 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)