Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-3)& = & 5 \color{red}{-} (12-5x) \\\Leftrightarrow & -18x-9& = &5-12+5x \\\Leftrightarrow & -18x \color{red}{-9} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -18x-5x& = &-7+9 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x-4)& = & 13 \color{red}{-} (8+x) \\\Leftrightarrow & -30x-24& = &13-8-x \\\Leftrightarrow & -30x \color{red}{-24} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &5+24 \\\Leftrightarrow & -29x& = &29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{29}{ \color{red}{-29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x+7)& = & 9 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+42& = &9-1-x \\\Leftrightarrow & -12x \color{red}{+42} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &8-42 \\\Leftrightarrow & -11x& = &-34 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-34}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{34}{11} & & \\ & V = \left\{ \frac{34}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x+7)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 18x+42& = &-10-3-x \\\Leftrightarrow & 18x \color{red}{+42} & = &-13 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 18x+x& = &-13-42 \\\Leftrightarrow & 19x& = &-55 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-55}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-55}{19} & & \\ & V = \left\{ \frac{-55}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-6)& = & -9 \color{red}{+} (-10+x) \\\Leftrightarrow & -30x-30& = &-9-10+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-19+30 \\\Leftrightarrow & -31x& = &11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-11}{31} & & \\ & V = \left\{ \frac{-11}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+4)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & 5x+20& = &9+4-x \\\Leftrightarrow & 5x \color{red}{+20} & = &13 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 5x+x& = &13-20 \\\Leftrightarrow & 6x& = &-7 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-7}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-7}{6} & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+4)& = & -8 \color{red}{-} (-12+x) \\\Leftrightarrow & -8x+16& = &-8+12-x \\\Leftrightarrow & -8x \color{red}{+16} & = &4 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &4-16 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-3)& = & -2 \color{red}{+} (10+x) \\\Leftrightarrow & -10x-6& = &-2+10+x \\\Leftrightarrow & -10x \color{red}{-6} & = &8 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -10x-x& = &8+6 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+1)& = & -7 \color{red}{-} (6-3x) \\\Leftrightarrow & -4x+4& = &-7-6+3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -4x-3x& = &-13-4 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-1)& = & -7 \color{red}{+} (-14+x) \\\Leftrightarrow & 20x-5& = &-7-14+x \\\Leftrightarrow & 20x \color{red}{-5} & = &-21 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 20x-x& = &-21+5 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x-5)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & -2x-10& = &1+4+x \\\Leftrightarrow & -2x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -2x-x& = &5+10 \\\Leftrightarrow & -3x& = &15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{15}{ \color{red}{-3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+2)& = & -14 \color{red}{-} (-12+x) \\\Leftrightarrow & 3x+6& = &-14+12-x \\\Leftrightarrow & 3x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 3x+x& = &-2-6 \\\Leftrightarrow & 4x& = &-8 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-8}{ \color{red}{4} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)