Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{11})& = & 3x+\frac{7}{11} \\\Leftrightarrow & -14x-\frac{14}{11}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x- \frac{14}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{-14} & = & \color{red}{33x} +7 \\\Leftrightarrow & -154x \color{red}{-14} \color{blue}{+14} \color{blue}{-33x} & = & \color{red}{33x} +7 \color{blue}{-33x} \color{blue}{+14} \\\Leftrightarrow & -154x-33x& = & 7+14 \\\Leftrightarrow & \color{red}{-187} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-187} & & \\\Leftrightarrow & x = \frac{-21}{187} & & \\ & V = \left\{ \frac{-21}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+44} & = & \color{red}{385x} +30 \\\Leftrightarrow & -330x \color{red}{+44} \color{blue}{-44} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-44} \\\Leftrightarrow & -330x-385x& = & 30-44 \\\Leftrightarrow & \color{red}{-715} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-715} & & \\\Leftrightarrow & x = \frac{14}{715} & & \\ & V = \left\{ \frac{14}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & 8x+\frac{3}{5} \\\Leftrightarrow & 21x+\frac{21}{11}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x+ \frac{105}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{440x} +33 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{-105} \\\Leftrightarrow & 1155x-440x& = & 33-105 \\\Leftrightarrow & \color{red}{715} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{715} & & \\ & V = \left\{ \frac{-72}{715} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & 300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 300x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{230} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{230} & & \\ & V = \left\{ \frac{-9}{230} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{385x} +20 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1650x-385x& = & 20-132 \\\Leftrightarrow & \color{red}{1265} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{1265} & & \\ & V = \left\{ \frac{-112}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+54} & = & \color{red}{-225x} +50 \\\Leftrightarrow & -405x \color{red}{+54} \color{blue}{-54} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-54} \\\Leftrightarrow & -405x+225x& = & 50-54 \\\Leftrightarrow & \color{red}{-180} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-180} & & \\\Leftrightarrow & x = \frac{1}{45} & & \\ & V = \left\{ \frac{1}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-2)& = & 3x+\frac{4}{7} \\\Leftrightarrow & -35x+14& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-245}{ \color{blue}{7} }x+ \frac{98}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -245x \color{red}{+98} & = & \color{red}{21x} +4 \\\Leftrightarrow & -245x \color{red}{+98} \color{blue}{-98} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-98} \\\Leftrightarrow & -245x-21x& = & 4-98 \\\Leftrightarrow & \color{red}{-266} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-266} & & \\\Leftrightarrow & x = \frac{47}{133} & & \\ & V = \left\{ \frac{47}{133} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+36} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -264x \color{red}{+36} \color{blue}{-36} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{-36} \\\Leftrightarrow & -264x+297x& = & 110-36 \\\Leftrightarrow & \color{red}{33} x& = & 74 \\\Leftrightarrow & x = \frac{74}{33} & & \\ & V = \left\{ \frac{74}{33} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{16}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+48} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 252x \color{red}{+48} \color{blue}{-48} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-48} \\\Leftrightarrow & 252x+105x& = & 14-48 \\\Leftrightarrow & \color{red}{357} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{357} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 1320x+275x& = & 30+132 \\\Leftrightarrow & \color{red}{1595} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1595} & & \\ & V = \left\{ \frac{162}{1595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{11})& = & -7x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 704x \color{red}{+64} & = & \color{red}{-616x} +99 \\\Leftrightarrow & 704x \color{red}{+64} \color{blue}{-64} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{-64} \\\Leftrightarrow & 704x+616x& = & 99-64 \\\Leftrightarrow & \color{red}{1320} x& = & 35 \\\Leftrightarrow & x = \frac{35}{1320} & & \\\Leftrightarrow & x = \frac{7}{264} & & \\ & V = \left\{ \frac{7}{264} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-60} & = & \color{red}{-40x} +7 \\\Leftrightarrow & -96x \color{red}{-60} \color{blue}{+60} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{+60} \\\Leftrightarrow & -96x+40x& = & 7+60 \\\Leftrightarrow & \color{red}{-56} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-56} & & \\\Leftrightarrow & x = \frac{-67}{56} & & \\ & V = \left\{ \frac{-67}{56} \right\} & \\\end{align}\)