Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{8}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+88} & = & \color{red}{385x} +20 \\\Leftrightarrow & 880x \color{red}{+88} \color{blue}{-88} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-88} \\\Leftrightarrow & 880x-385x& = & 20-88 \\\Leftrightarrow & \color{red}{495} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{495} & & \\ & V = \left\{ \frac{-68}{495} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+330} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -1848x+385x& = & 35-330 \\\Leftrightarrow & \color{red}{-1463} x& = & -295 \\\Leftrightarrow & x = \frac{-295}{-1463} & & \\\Leftrightarrow & x = \frac{295}{1463} & & \\ & V = \left\{ \frac{295}{1463} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+84} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & -1050x+245x& = & 50-84 \\\Leftrightarrow & \color{red}{-805} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-805} & & \\\Leftrightarrow & x = \frac{34}{805} & & \\ & V = \left\{ \frac{34}{805} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{6})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{25}{6}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+125} & = & \color{red}{-270x} +36 \\\Leftrightarrow & 600x \color{red}{+125} \color{blue}{-125} \color{blue}{+270x} & = & \color{red}{-270x} +36 \color{blue}{+270x} \color{blue}{-125} \\\Leftrightarrow & 600x+270x& = & 36-125 \\\Leftrightarrow & \color{red}{870} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{870} & & \\ & V = \left\{ \frac{-89}{870} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -20x+\frac{15}{4}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{-196x} +12 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +12 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & -560x+196x& = & 12-105 \\\Leftrightarrow & \color{red}{-364} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-364} & & \\\Leftrightarrow & x = \frac{93}{364} & & \\ & V = \left\{ \frac{93}{364} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{35x} +7 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +7 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 60x-35x& = & 7-12 \\\Leftrightarrow & \color{red}{25} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{25} & & \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -4x+\frac{8}{9} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -4x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-144}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{-135} & = & \color{red}{-144x} +32 \\\Leftrightarrow & 540x \color{red}{-135} \color{blue}{+135} \color{blue}{+144x} & = & \color{red}{-144x} +32 \color{blue}{+144x} \color{blue}{+135} \\\Leftrightarrow & 540x+144x& = & 32+135 \\\Leftrightarrow & \color{red}{684} x& = & 167 \\\Leftrightarrow & x = \frac{167}{684} & & \\ & V = \left\{ \frac{167}{684} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{-18} & = & \color{red}{77x} +6 \\\Leftrightarrow & 264x \color{red}{-18} \color{blue}{+18} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+18} \\\Leftrightarrow & 264x-77x& = & 6+18 \\\Leftrightarrow & \color{red}{187} x& = & 24 \\\Leftrightarrow & x = \frac{24}{187} & & \\ & V = \left\{ \frac{24}{187} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{100x} +16 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{-100x} & = & \color{red}{100x} +16 \color{blue}{-100x} \color{blue}{+75} \\\Leftrightarrow & -240x-100x& = & 16+75 \\\Leftrightarrow & \color{red}{-340} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-340} & & \\\Leftrightarrow & x = \frac{-91}{340} & & \\ & V = \left\{ \frac{-91}{340} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-90} & = & \color{red}{105x} +14 \\\Leftrightarrow & 504x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & 504x-105x& = & 14+90 \\\Leftrightarrow & \color{red}{399} x& = & 104 \\\Leftrightarrow & x = \frac{104}{399} & & \\ & V = \left\{ \frac{104}{399} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{1}{3})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -14x+\frac{7}{3}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+70} & = & \color{red}{-90x} +21 \\\Leftrightarrow & -420x \color{red}{+70} \color{blue}{-70} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{-70} \\\Leftrightarrow & -420x+90x& = & 21-70 \\\Leftrightarrow & \color{red}{-330} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-330} & & \\\Leftrightarrow & x = \frac{49}{330} & & \\ & V = \left\{ \frac{49}{330} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+88} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -132x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & -132x+297x& = & 18-88 \\\Leftrightarrow & \color{red}{165} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{165} & & \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)