Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-42} & = & \color{red}{-539x} +99 \\\Leftrightarrow & -770x \color{red}{-42} \color{blue}{+42} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{+42} \\\Leftrightarrow & -770x+539x& = & 99+42 \\\Leftrightarrow & \color{red}{-231} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-231} & & \\\Leftrightarrow & x = \frac{-47}{77} & & \\ & V = \left\{ \frac{-47}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-20} \\\Leftrightarrow & 112x+49x& = & 10-20 \\\Leftrightarrow & \color{red}{161} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{161} & & \\ & V = \left\{ \frac{-10}{161} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -4x+\frac{6}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{+6} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -20x \color{red}{+6} \color{blue}{-6} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-6} \\\Leftrightarrow & -20x+45x& = & 6-6 \\\Leftrightarrow & \color{red}{25} x& = & 0 \\\Leftrightarrow & x = \frac{0}{25} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-18} & = & \color{red}{55x} +8 \\\Leftrightarrow & 132x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & 132x-55x& = & 8+18 \\\Leftrightarrow & \color{red}{77} x& = & 26 \\\Leftrightarrow & x = \frac{26}{77} & & \\ & V = \left\{ \frac{26}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{504}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 504x \color{red}{+120} & = & \color{red}{140x} +21 \\\Leftrightarrow & 504x \color{red}{+120} \color{blue}{-120} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-120} \\\Leftrightarrow & 504x-140x& = & 21-120 \\\Leftrightarrow & \color{red}{364} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{364} & & \\ & V = \left\{ \frac{-99}{364} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{-49x} +3 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & 210x+49x& = & 3-30 \\\Leftrightarrow & \color{red}{259} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{259} & & \\ & V = \left\{ \frac{-27}{259} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{+63} & = & \color{red}{-216x} +64 \\\Leftrightarrow & -840x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +64 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & -840x+216x& = & 64-63 \\\Leftrightarrow & \color{red}{-624} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-624} & & \\\Leftrightarrow & x = \frac{-1}{624} & & \\ & V = \left\{ \frac{-1}{624} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{5})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{-45x} +40 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{+45x} & = & \color{red}{-45x} +40 \color{blue}{+45x} \color{blue}{-42} \\\Leftrightarrow & -210x+45x& = & 40-42 \\\Leftrightarrow & \color{red}{-165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-165} & & \\\Leftrightarrow & x = \frac{2}{165} & & \\ & V = \left\{ \frac{2}{165} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 330x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 330x+275x& = & 25-132 \\\Leftrightarrow & \color{red}{605} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{605} & & \\ & V = \left\{ \frac{-107}{605} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -8x+\frac{7}{2} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -8x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{-48x} +21 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{+48x} & = & \color{red}{-48x} +21 \color{blue}{+48x} \color{blue}{-28} \\\Leftrightarrow & 126x+48x& = & 21-28 \\\Leftrightarrow & \color{red}{174} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{174} & & \\ & V = \left\{ \frac{-7}{174} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{4}{11})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{28}{11}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{84}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+84} & = & \color{red}{132x} +44 \\\Leftrightarrow & -924x \color{red}{+84} \color{blue}{-84} \color{blue}{-132x} & = & \color{red}{132x} +44 \color{blue}{-132x} \color{blue}{-84} \\\Leftrightarrow & -924x-132x& = & 44-84 \\\Leftrightarrow & \color{red}{-1056} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1056} & & \\\Leftrightarrow & x = \frac{5}{132} & & \\ & V = \left\{ \frac{5}{132} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+168} & = & \color{red}{175x} +40 \\\Leftrightarrow & 840x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & 840x-175x& = & 40-168 \\\Leftrightarrow & \color{red}{665} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{665} & & \\ & V = \left\{ \frac{-128}{665} \right\} & \\\end{align}\)