Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-1)& = & 4 \color{red}{-} (-1+x) \\\Leftrightarrow & 5x-5& = &4+1-x \\\Leftrightarrow & 5x \color{red}{-5} & = &5 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 5x+x& = &5+5 \\\Leftrightarrow & 6x& = &10 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{10}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x+2)& = & -3 \color{red}{+} (-3+x) \\\Leftrightarrow & -18x+6& = &-3-3+x \\\Leftrightarrow & -18x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &-6-6 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-5)& = & -12 \color{red}{-} (12+3x) \\\Leftrightarrow & -16x-20& = &-12-12-3x \\\Leftrightarrow & -16x \color{red}{-20} & = &-24 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -16x+3x& = &-24+20 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+2)& = & -12 \color{red}{+} (3+x) \\\Leftrightarrow & -30x+12& = &-12+3+x \\\Leftrightarrow & -30x \color{red}{+12} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &-9-12 \\\Leftrightarrow & -31x& = &-21 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-21}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-4)& = & -14 \color{red}{+} (-11-5x) \\\Leftrightarrow & 8x-8& = &-14-11-5x \\\Leftrightarrow & 8x \color{red}{-8} & = &-25 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 8x+5x& = &-25+8 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x+4)& = & -12 \color{red}{+} (-3+x) \\\Leftrightarrow & 20x+16& = &-12-3+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-15 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-15-16 \\\Leftrightarrow & 19x& = &-31 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-31}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-31}{19} & & \\ & V = \left\{ \frac{-31}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+4)& = & 10 \color{red}{-} (-13-3x) \\\Leftrightarrow & -4x+8& = &10+13+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &23 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &23 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &23-8 \\\Leftrightarrow & -7x& = &15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x+3)& = & -11 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x+9& = &-11+3-x \\\Leftrightarrow & 12x \color{red}{+9} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &-8-9 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x-6)& = & 1 \color{red}{+} (7+3x) \\\Leftrightarrow & -10x-30& = &1+7+3x \\\Leftrightarrow & -10x \color{red}{-30} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & -10x-3x& = &8+30 \\\Leftrightarrow & -13x& = &38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-6)& = & -8 \color{red}{+} (10+x) \\\Leftrightarrow & -24x-24& = &-8+10+x \\\Leftrightarrow & -24x \color{red}{-24} & = &2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -24x-x& = &2+24 \\\Leftrightarrow & -25x& = &26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-26}{25} & & \\ & V = \left\{ \frac{-26}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+5)& = & 1 \color{red}{+} (-12-5x) \\\Leftrightarrow & 36x+30& = &1-12-5x \\\Leftrightarrow & 36x \color{red}{+30} & = &-11 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 36x+5x& = &-11-30 \\\Leftrightarrow & 41x& = &-41 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-41}{ \color{red}{41} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+7)& = & 12 \color{red}{-} (-11+x) \\\Leftrightarrow & -12x+21& = &12+11-x \\\Leftrightarrow & -12x \color{red}{+21} & = &23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &23-21 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)