Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x-5)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & -20x-25& = &-15+8-x \\\Leftrightarrow & -20x \color{red}{-25} & = &-7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -20x+x& = &-7+25 \\\Leftrightarrow & -19x& = &18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-18}{19} & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+5)& = & -13 \color{red}{-} (1-4x) \\\Leftrightarrow & 5x+25& = &-13-1+4x \\\Leftrightarrow & 5x \color{red}{+25} & = &-14 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 5x-4x& = &-14-25 \\\Leftrightarrow & x& = &-39 \\ & V = \left\{ -39 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+1)& = & -1 \color{red}{-} (13+2x) \\\Leftrightarrow & -15x+5& = &-1-13-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-14 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &-14-5 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x+1)& = & 14 \color{red}{-} (-5+x) \\\Leftrightarrow & -16x+4& = &14+5-x \\\Leftrightarrow & -16x \color{red}{+4} & = &19 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -16x+x& = &19-4 \\\Leftrightarrow & -15x& = &15 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{15}{ \color{red}{-15} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+1)& = & 11 \color{red}{+} (-9-3x) \\\Leftrightarrow & -10x+2& = &11-9-3x \\\Leftrightarrow & -10x \color{red}{+2} & = &2 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -10x+3x& = &2-2 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+5)& = & -12 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+20& = &-12+6-x \\\Leftrightarrow & 12x \color{red}{+20} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 12x+x& = &-6-20 \\\Leftrightarrow & 13x& = &-26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-26}{ \color{red}{13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+6)& = & -3 \color{red}{+} (1+x) \\\Leftrightarrow & 30x+36& = &-3+1+x \\\Leftrightarrow & 30x \color{red}{+36} & = &-2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &-2-36 \\\Leftrightarrow & 29x& = &-38 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-38}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-38}{29} & & \\ & V = \left\{ \frac{-38}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-5)& = & -15 \color{red}{-} (-8+3x) \\\Leftrightarrow & 20x-20& = &-15+8-3x \\\Leftrightarrow & 20x \color{red}{-20} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 20x+3x& = &-7+20 \\\Leftrightarrow & 23x& = &13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-6)& = & 12 \color{red}{+} (11+x) \\\Leftrightarrow & -20x-24& = &12+11+x \\\Leftrightarrow & -20x \color{red}{-24} & = &23 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &23+24 \\\Leftrightarrow & -21x& = &47 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{47}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-47}{21} & & \\ & V = \left\{ \frac{-47}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-5)& = & -11 \color{red}{-} (-15+x) \\\Leftrightarrow & -20x-20& = &-11+15-x \\\Leftrightarrow & -20x \color{red}{-20} & = &4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -20x+x& = &4+20 \\\Leftrightarrow & -19x& = &24 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{24}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-2)& = & -14 \color{red}{+} (9+x) \\\Leftrightarrow & 36x-12& = &-14+9+x \\\Leftrightarrow & 36x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 36x-x& = &-5+12 \\\Leftrightarrow & 35x& = &7 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{7}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+4)& = & -10 \color{red}{+} (7+x) \\\Leftrightarrow & -20x+16& = &-10+7+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-3 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-3-16 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)