Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-1)& = & 2 \color{red}{+} (15-2x) \\\Leftrightarrow & -15x-3& = &2+15-2x \\\Leftrightarrow & -15x \color{red}{-3} & = &17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -15x+2x& = &17+3 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-4)& = & -5 \color{red}{+} (1+x) \\\Leftrightarrow & -4x-16& = &-5+1+x \\\Leftrightarrow & -4x \color{red}{-16} & = &-4 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &-4+16 \\\Leftrightarrow & -5x& = &12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+1)& = & 3 \color{red}{-} (-4+x) \\\Leftrightarrow & -18x+3& = &3+4-x \\\Leftrightarrow & -18x \color{red}{+3} & = &7 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -18x+x& = &7-3 \\\Leftrightarrow & -17x& = &4 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{4}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x+2)& = & 15 \color{red}{+} (3+x) \\\Leftrightarrow & -2x+4& = &15+3+x \\\Leftrightarrow & -2x \color{red}{+4} & = &18 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -2x-x& = &18-4 \\\Leftrightarrow & -3x& = &14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+7)& = & -13 \color{red}{+} (14-4x) \\\Leftrightarrow & -9x+21& = &-13+14-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &1-21 \\\Leftrightarrow & -5x& = &-20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-20}{ \color{red}{-5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-2)& = & 11 \color{red}{-} (-14+x) \\\Leftrightarrow & 18x-12& = &11+14-x \\\Leftrightarrow & 18x \color{red}{-12} & = &25 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &25+12 \\\Leftrightarrow & 19x& = &37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{37}{19} & & \\ & V = \left\{ \frac{37}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-2)& = & 11 \color{red}{-} (15+x) \\\Leftrightarrow & -18x-12& = &11-15-x \\\Leftrightarrow & -18x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &-4+12 \\\Leftrightarrow & -17x& = &8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+1)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & 2x+2& = &-3+9+x \\\Leftrightarrow & 2x \color{red}{+2} & = &6 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 2x-x& = &6-2 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-4)& = & -5 \color{red}{+} (11-5x) \\\Leftrightarrow & 8x-8& = &-5+11-5x \\\Leftrightarrow & 8x \color{red}{-8} & = &6 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 8x+5x& = &6+8 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x+3)& = & 10 \color{red}{+} (-9-5x) \\\Leftrightarrow & 8x+6& = &10-9-5x \\\Leftrightarrow & 8x \color{red}{+6} & = &1 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 8x+5x& = &1-6 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-4)& = & -10 \color{red}{+} (-12+x) \\\Leftrightarrow & 36x-24& = &-10-12+x \\\Leftrightarrow & 36x \color{red}{-24} & = &-22 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 36x-x& = &-22+24 \\\Leftrightarrow & 35x& = &2 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{2}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+1)& = & 6 \color{red}{+} (9+4x) \\\Leftrightarrow & 3x+3& = &6+9+4x \\\Leftrightarrow & 3x \color{red}{+3} & = &15 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & 3x-4x& = &15-3 \\\Leftrightarrow & -x& = &12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{12}{ \color{red}{-1} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)