Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+7)& = & -11 \color{red}{-} (4-3x) \\\Leftrightarrow & 4x+14& = &-11-4+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &-15 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &-15-14 \\\Leftrightarrow & x& = &-29 \\ & V = \left\{ -29 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-5)& = & -9 \color{red}{-} (15-2x) \\\Leftrightarrow & -15x-25& = &-9-15+2x \\\Leftrightarrow & -15x \color{red}{-25} & = &-24 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-24 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -15x-2x& = &-24+25 \\\Leftrightarrow & -17x& = &1 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{1}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x-5)& = & -13 \color{red}{-} (6+x) \\\Leftrightarrow & -12x-30& = &-13-6-x \\\Leftrightarrow & -12x \color{red}{-30} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -12x+x& = &-19+30 \\\Leftrightarrow & -11x& = &11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{11}{ \color{red}{-11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-1)& = & 4 \color{red}{-} (-4+x) \\\Leftrightarrow & -2x-2& = &4+4-x \\\Leftrightarrow & -2x \color{red}{-2} & = &8 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &8+2 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-4)& = & 11 \color{red}{+} (4+x) \\\Leftrightarrow & -12x-8& = &11+4+x \\\Leftrightarrow & -12x \color{red}{-8} & = &15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &15+8 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x-6)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x-24& = &-2-9+x \\\Leftrightarrow & -8x \color{red}{-24} & = &-11 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -8x-x& = &-11+24 \\\Leftrightarrow & -9x& = &13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+4)& = & 13 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x+12& = &13-11-5x \\\Leftrightarrow & -18x \color{red}{+12} & = &2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -18x+5x& = &2-12 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-2)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & 8x-4& = &13+14+x \\\Leftrightarrow & 8x \color{red}{-4} & = &27 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 8x-x& = &27+4 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-2)& = & 2 \color{red}{-} (-1-3x) \\\Leftrightarrow & -4x-4& = &2+1+3x \\\Leftrightarrow & -4x \color{red}{-4} & = &3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -4x-3x& = &3+4 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-1)& = & 11 \color{red}{-} (-14-5x) \\\Leftrightarrow & 8x-4& = &11+14+5x \\\Leftrightarrow & 8x \color{red}{-4} & = &25 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &25 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 8x-5x& = &25+4 \\\Leftrightarrow & 3x& = &29 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{29}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{29}{3} & & \\ & V = \left\{ \frac{29}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+7)& = & -10 \color{red}{+} (7+x) \\\Leftrightarrow & 20x+35& = &-10+7+x \\\Leftrightarrow & 20x \color{red}{+35} & = &-3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &-3-35 \\\Leftrightarrow & 19x& = &-38 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-38}{ \color{red}{19} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-1)& = & -8 \color{red}{-} (-9+3x) \\\Leftrightarrow & 10x-5& = &-8+9-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &1+5 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)