Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-1)& = & -2 \color{red}{+} (-3+x) \\\Leftrightarrow & 2x-2& = &-2-3+x \\\Leftrightarrow & 2x \color{red}{-2} & = &-5 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 2x-x& = &-5+2 \\\Leftrightarrow & x& = &-3 \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-5)& = & 15 \color{red}{-} (-4+x) \\\Leftrightarrow & -10x-25& = &15+4-x \\\Leftrightarrow & -10x \color{red}{-25} & = &19 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -10x+x& = &19+25 \\\Leftrightarrow & -9x& = &44 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{44}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-44}{9} & & \\ & V = \left\{ \frac{-44}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-1)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & -24x-6& = &-10+8+x \\\Leftrightarrow & -24x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -24x-x& = &-2+6 \\\Leftrightarrow & -25x& = &4 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{4}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+5)& = & -8 \color{red}{-} (15+3x) \\\Leftrightarrow & 20x+20& = &-8-15-3x \\\Leftrightarrow & 20x \color{red}{+20} & = &-23 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 20x+3x& = &-23-20 \\\Leftrightarrow & 23x& = &-43 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-43}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-43}{23} & & \\ & V = \left\{ \frac{-43}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+4)& = & -7 \color{red}{-} (12-2x) \\\Leftrightarrow & -3x+12& = &-7-12+2x \\\Leftrightarrow & -3x \color{red}{+12} & = &-19 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &-19 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & -3x-2x& = &-19-12 \\\Leftrightarrow & -5x& = &-31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-6)& = & 6 \color{red}{-} (-7-2x) \\\Leftrightarrow & 3x-18& = &6+7+2x \\\Leftrightarrow & 3x \color{red}{-18} & = &13 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & 3x-2x& = &13+18 \\\Leftrightarrow & x& = &31 \\ & V = \left\{ 31 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-5)& = & -12 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x-20& = &-12+8-x \\\Leftrightarrow & 12x \color{red}{-20} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &-4+20 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-5)& = & -6 \color{red}{+} (-7+x) \\\Leftrightarrow & -20x-20& = &-6-7+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-13+20 \\\Leftrightarrow & -21x& = &7 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{7}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-4)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & -8x-8& = &12-5-x \\\Leftrightarrow & -8x \color{red}{-8} & = &7 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &7+8 \\\Leftrightarrow & -7x& = &15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-6)& = & -12 \color{red}{-} (5+x) \\\Leftrightarrow & -20x-30& = &-12-5-x \\\Leftrightarrow & -20x \color{red}{-30} & = &-17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &-17+30 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x-1)& = & 5 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-6& = &5-7+x \\\Leftrightarrow & 12x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &-2+6 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+4)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x+16& = &-11-14+x \\\Leftrightarrow & 24x \color{red}{+16} & = &-25 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &-25-16 \\\Leftrightarrow & 23x& = &-41 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-41}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-41}{23} & & \\ & V = \left\{ \frac{-41}{23} \right\} & \\\end{align}\)