Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+1)& = & -8 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x+3& = &-8-13+x \\\Leftrightarrow & -12x \color{red}{+3} & = &-21 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &-21-3 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+7)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & 6x+21& = &2+10+x \\\Leftrightarrow & 6x \color{red}{+21} & = &12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 6x-x& = &12-21 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-5)& = & -4 \color{red}{-} (8+x) \\\Leftrightarrow & 18x-15& = &-4-8-x \\\Leftrightarrow & 18x \color{red}{-15} & = &-12 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 18x+x& = &-12+15 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-1)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-3& = &-13+15+x \\\Leftrightarrow & -12x \color{red}{-3} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &2+3 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-7)& = & 9 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-14& = &9+15+x \\\Leftrightarrow & -12x \color{red}{-14} & = &24 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -12x-x& = &24+14 \\\Leftrightarrow & -13x& = &38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-2)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & -20x-10& = &-15+9+x \\\Leftrightarrow & -20x \color{red}{-10} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -20x-x& = &-6+10 \\\Leftrightarrow & -21x& = &4 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{4}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+4)& = & 14 \color{red}{+} (13+x) \\\Leftrightarrow & -18x+12& = &14+13+x \\\Leftrightarrow & -18x \color{red}{+12} & = &27 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &27-12 \\\Leftrightarrow & -19x& = &15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+4)& = & 6 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x+24& = &6+4-x \\\Leftrightarrow & 24x \color{red}{+24} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &10-24 \\\Leftrightarrow & 25x& = &-14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+6)& = & -6 \color{red}{+} (13+2x) \\\Leftrightarrow & 15x+30& = &-6+13+2x \\\Leftrightarrow & 15x \color{red}{+30} & = &7 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 15x-2x& = &7-30 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+1)& = & 15 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x+4& = &15+11-x \\\Leftrightarrow & 24x \color{red}{+4} & = &26 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 24x+x& = &26-4 \\\Leftrightarrow & 25x& = &22 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{22}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{22}{25} & & \\ & V = \left\{ \frac{22}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+1)& = & -2 \color{red}{+} (-7+x) \\\Leftrightarrow & 36x+6& = &-2-7+x \\\Leftrightarrow & 36x \color{red}{+6} & = &-9 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 36x-x& = &-9-6 \\\Leftrightarrow & 35x& = &-15 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-15}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+6)& = & -13 \color{red}{+} (12+x) \\\Leftrightarrow & 4x+24& = &-13+12+x \\\Leftrightarrow & 4x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 4x-x& = &-1-24 \\\Leftrightarrow & 3x& = &-25 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-25}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-25}{3} & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)