Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-6)& = & 10 \color{red}{-} (2+x) \\\Leftrightarrow & -10x-30& = &10-2-x \\\Leftrightarrow & -10x \color{red}{-30} & = &8 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -10x+x& = &8+30 \\\Leftrightarrow & -9x& = &38 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{38}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-38}{9} & & \\ & V = \left\{ \frac{-38}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x-6)& = & 4 \color{red}{-} (7+x) \\\Leftrightarrow & 20x-30& = &4-7-x \\\Leftrightarrow & 20x \color{red}{-30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 20x+x& = &-3+30 \\\Leftrightarrow & 21x& = &27 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{27}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+4)& = & 5 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x+20& = &5-14-2x \\\Leftrightarrow & 15x \color{red}{+20} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 15x+2x& = &-9-20 \\\Leftrightarrow & 17x& = &-29 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-29}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-29}{17} & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+2)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & 8x+4& = &2+13+x \\\Leftrightarrow & 8x \color{red}{+4} & = &15 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 8x-x& = &15-4 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-3)& = & -1 \color{red}{-} (-6+x) \\\Leftrightarrow & 8x-6& = &-1+6-x \\\Leftrightarrow & 8x \color{red}{-6} & = &5 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 8x+x& = &5+6 \\\Leftrightarrow & 9x& = &11 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{11}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{11}{9} & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x+1)& = & -9 \color{red}{+} (-7-3x) \\\Leftrightarrow & -10x+5& = &-9-7-3x \\\Leftrightarrow & -10x \color{red}{+5} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & -10x+3x& = &-16-5 \\\Leftrightarrow & -7x& = &-21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-21}{ \color{red}{-7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-4)& = & 13 \color{red}{+} (11+x) \\\Leftrightarrow & 12x-16& = &13+11+x \\\Leftrightarrow & 12x \color{red}{-16} & = &24 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &24+16 \\\Leftrightarrow & 11x& = &40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{40}{11} & & \\ & V = \left\{ \frac{40}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-7)& = & 4 \color{red}{+} (4-5x) \\\Leftrightarrow & -16x-28& = &4+4-5x \\\Leftrightarrow & -16x \color{red}{-28} & = &8 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+28} \\\Leftrightarrow & -16x+5x& = &8+28 \\\Leftrightarrow & -11x& = &36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+6)& = & 13 \color{red}{-} (1+x) \\\Leftrightarrow & -2x+12& = &13-1-x \\\Leftrightarrow & -2x \color{red}{+12} & = &12 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -2x+x& = &12-12 \\\Leftrightarrow & -x& = &0 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{0}{ \color{red}{-1} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x+1)& = & -14 \color{red}{-} (14+x) \\\Leftrightarrow & 6x+2& = &-14-14-x \\\Leftrightarrow & 6x \color{red}{+2} & = &-28 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 6x+x& = &-28-2 \\\Leftrightarrow & 7x& = &-30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x+1)& = & -8 \color{red}{+} (5+x) \\\Leftrightarrow & 30x+5& = &-8+5+x \\\Leftrightarrow & 30x \color{red}{+5} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &-3-5 \\\Leftrightarrow & 29x& = &-8 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-8}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-8}{29} & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+5)& = & 1 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x+10& = &1-6+x \\\Leftrightarrow & 12x \color{red}{+10} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 12x-x& = &-5-10 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)