Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x-5)& = & -13 \color{red}{+} (-3-3x) \\\Leftrightarrow & -4x-20& = &-13-3-3x \\\Leftrightarrow & -4x \color{red}{-20} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -4x+3x& = &-16+20 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+6)& = & -9 \color{red}{+} (11+3x) \\\Leftrightarrow & -8x+12& = &-9+11+3x \\\Leftrightarrow & -8x \color{red}{+12} & = &2 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -8x-3x& = &2-12 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+4)& = & -13 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+8& = &-13+5+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-8-8 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+1)& = & 7 \color{red}{-} (-5-3x) \\\Leftrightarrow & 4x+2& = &7+5+3x \\\Leftrightarrow & 4x \color{red}{+2} & = &12 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 4x-3x& = &12-2 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x+7)& = & 11 \color{red}{-} (-8-5x) \\\Leftrightarrow & 8x+14& = &11+8+5x \\\Leftrightarrow & 8x \color{red}{+14} & = &19 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & 8x-5x& = &19-14 \\\Leftrightarrow & 3x& = &5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+7)& = & 10 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+14& = &10-9+x \\\Leftrightarrow & 12x \color{red}{+14} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 12x-x& = &1-14 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-7)& = & -6 \color{red}{+} (-3-5x) \\\Leftrightarrow & -8x-14& = &-6-3-5x \\\Leftrightarrow & -8x \color{red}{-14} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & -8x+5x& = &-9+14 \\\Leftrightarrow & -3x& = &5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-7)& = & 5 \color{red}{+} (10-4x) \\\Leftrightarrow & 9x-21& = &5+10-4x \\\Leftrightarrow & 9x \color{red}{-21} & = &15 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 9x+4x& = &15+21 \\\Leftrightarrow & 13x& = &36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-6)& = & 14 \color{red}{+} (14+x) \\\Leftrightarrow & -12x-24& = &14+14+x \\\Leftrightarrow & -12x \color{red}{-24} & = &28 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &28+24 \\\Leftrightarrow & -13x& = &52 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{52}{ \color{red}{-13} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x+3)& = & 8 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+12& = &8+10-x \\\Leftrightarrow & -12x \color{red}{+12} & = &18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &18-12 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-3)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & -36x-18& = &-10+14-x \\\Leftrightarrow & -36x \color{red}{-18} & = &4 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -36x+x& = &4+18 \\\Leftrightarrow & -35x& = &22 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{22}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-22}{35} & & \\ & V = \left\{ \frac{-22}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-4)& = & -9 \color{red}{-} (-7+x) \\\Leftrightarrow & 18x-24& = &-9+7-x \\\Leftrightarrow & 18x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 18x+x& = &-2+24 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)