Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x+6)& = & -14 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x+36& = &-14+9-x \\\Leftrightarrow & -12x \color{red}{+36} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -12x+x& = &-5-36 \\\Leftrightarrow & -11x& = &-41 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-41}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{41}{11} & & \\ & V = \left\{ \frac{41}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x-6)& = & -8 \color{red}{-} (-13+x) \\\Leftrightarrow & 20x-24& = &-8+13-x \\\Leftrightarrow & 20x \color{red}{-24} & = &5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &5+24 \\\Leftrightarrow & 21x& = &29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x+6)& = & 15 \color{red}{-} (-3+x) \\\Leftrightarrow & -20x+30& = &15+3-x \\\Leftrightarrow & -20x \color{red}{+30} & = &18 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -20x+x& = &18-30 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-6)& = & 8 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-24& = &8-7+x \\\Leftrightarrow & -12x \color{red}{-24} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &1+24 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+4)& = & 11 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x+24& = &11-9+x \\\Leftrightarrow & 24x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &2-24 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+5)& = & 5 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+15& = &5-13-x \\\Leftrightarrow & 12x \color{red}{+15} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 12x+x& = &-8-15 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-4)& = & 9 \color{red}{+} (13-2x) \\\Leftrightarrow & -15x-12& = &9+13-2x \\\Leftrightarrow & -15x \color{red}{-12} & = &22 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &22 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -15x+2x& = &22+12 \\\Leftrightarrow & -13x& = &34 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{34}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-34}{13} & & \\ & V = \left\{ \frac{-34}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x-7)& = & -10 \color{red}{+} (11+x) \\\Leftrightarrow & -12x-14& = &-10+11+x \\\Leftrightarrow & -12x \color{red}{-14} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -12x-x& = &1+14 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+4)& = & -9 \color{red}{-} (-12-5x) \\\Leftrightarrow & -18x+12& = &-9+12+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &3 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &3-12 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+1)& = & -11 \color{red}{+} (-9+x) \\\Leftrightarrow & -20x+5& = &-11-9+x \\\Leftrightarrow & -20x \color{red}{+5} & = &-20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -20x-x& = &-20-5 \\\Leftrightarrow & -21x& = &-25 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-25}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{25}{21} & & \\ & V = \left\{ \frac{25}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x-7)& = & 12 \color{red}{+} (2+x) \\\Leftrightarrow & -8x-28& = &12+2+x \\\Leftrightarrow & -8x \color{red}{-28} & = &14 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -8x-x& = &14+28 \\\Leftrightarrow & -9x& = &42 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{42}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-7)& = & 12 \color{red}{+} (-1-3x) \\\Leftrightarrow & -10x-35& = &12-1-3x \\\Leftrightarrow & -10x \color{red}{-35} & = &11 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & -10x+3x& = &11+35 \\\Leftrightarrow & -7x& = &46 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{46}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-46}{7} & & \\ & V = \left\{ \frac{-46}{7} \right\} & \\\end{align}\)