Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-2)& = & 11 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-12& = &11-8+x \\\Leftrightarrow & -30x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &3+12 \\\Leftrightarrow & -31x& = &15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x+6)& = & 7 \color{red}{+} (-7-5x) \\\Leftrightarrow & -6x+36& = &7-7-5x \\\Leftrightarrow & -6x \color{red}{+36} & = &0 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -6x+5x& = &0-36 \\\Leftrightarrow & -x& = &-36 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-36}{ \color{red}{-1} } \\\Leftrightarrow & x = 36 & & \\ & V = \left\{ 36 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-3)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x-9& = &-10-15+x \\\Leftrightarrow & -12x \color{red}{-9} & = &-25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -12x-x& = &-25+9 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-5)& = & 5 \color{red}{-} (-9+x) \\\Leftrightarrow & 6x-15& = &5+9-x \\\Leftrightarrow & 6x \color{red}{-15} & = &14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &14+15 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+1)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x+4& = &7-9+x \\\Leftrightarrow & 20x \color{red}{+4} & = &-2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 20x-x& = &-2-4 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-3)& = & -15 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-9& = &-15-6+5x \\\Leftrightarrow & 18x \color{red}{-9} & = &-21 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &-21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & 18x-5x& = &-21+9 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-6)& = & 13 \color{red}{+} (10+x) \\\Leftrightarrow & 15x-30& = &13+10+x \\\Leftrightarrow & 15x \color{red}{-30} & = &23 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 15x-x& = &23+30 \\\Leftrightarrow & 14x& = &53 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{53}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{53}{14} & & \\ & V = \left\{ \frac{53}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x+4)& = & 9 \color{red}{-} (8+2x) \\\Leftrightarrow & -9x+12& = &9-8-2x \\\Leftrightarrow & -9x \color{red}{+12} & = &1 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -9x+2x& = &1-12 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-6)& = & 14 \color{red}{-} (15-3x) \\\Leftrightarrow & 4x-12& = &14-15+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &-1+12 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+7)& = & 3 \color{red}{-} (-8+x) \\\Leftrightarrow & -18x+21& = &3+8-x \\\Leftrightarrow & -18x \color{red}{+21} & = &11 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -18x+x& = &11-21 \\\Leftrightarrow & -17x& = &-10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-5)& = & 14 \color{red}{+} (14+4x) \\\Leftrightarrow & 5x-25& = &14+14+4x \\\Leftrightarrow & 5x \color{red}{-25} & = &28 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &28 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & 5x-4x& = &28+25 \\\Leftrightarrow & x& = &53 \\ & V = \left\{ 53 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+6)& = & 8 \color{red}{-} (15-3x) \\\Leftrightarrow & -16x+24& = &8-15+3x \\\Leftrightarrow & -16x \color{red}{+24} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -16x-3x& = &-7-24 \\\Leftrightarrow & -19x& = &-31 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-31}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{31}{19} & & \\ & V = \left\{ \frac{31}{19} \right\} & \\\end{align}\)