Pergunta

1.22 x+14=12 x+49 ( fin ) 2.18-9 x leq 40 3.5(x-8) geq (1)/(2)(4 x-8) 4.4 x-3(4 x-9) leq
Solução

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AfonsoEspecialista · Tutor por 3 anos
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Let's solve each equation or inequality step by step:<br /><br />1. \(1.22x + 14 = 12x + 49\)<br /><br />To solve this equation, we need to isolate the variable \(x\). First, let's move all the terms involving \(x\) to one side of the equation and the constant terms to the other side.<br /><br />Subtract \(1.22x\) from both sides:<br />\(14 = 10.78x + 49\)<br /><br />Next, subtract 49 from both sides:<br />\(-35 = 10.78x\)<br /><br />Finally, divide both sides by 10.78 to solve for \(x\):<br />\(x = -\frac{35}{10.78}\)<br /><br />2. \(18 - 9x \leq 40\)<br /><br />To solve this inequality, we need to isolate the variable \(x\). First, subtract 18 from both sides:<br />\(-9x \leq 22\)<br /><br />Next, divide both sides by -9. Remember that when dividing or multiplying an inequality by a negative number, the inequality sign flips:<br />\(x \geq -\frac{22}{9}\)<br /><br />3. \(5(x - 8) \geq \frac{1}{2}(4x - 8)\)<br /><br />First, distribute the 5 on the left side:<br />\(5x - 40 \geq 2x - 4\)<br /><br />Next, subtract \(2x\) from both sides:<br />\(3x - 40 \geq -4\)<br /><br />Add 40 to both sides:<br />\(3x \geq 36\)<br /><br />Finally, divide both sides by 3:<br />\(x \geq 12\)<br /><br />4. \(4x - 3(4x - 9) \leq 0\)<br /><br />First, distribute the -3 on the right side:<br />\(4x - 12x + 27 \leq 0\)<br /><br />Combine like terms:<br />\(-8x + 27 \leq 0\)<br /><br />Subtract 27 from both sides:<br />\(-8x \leq -27\)<br /><br />Finally, divide both sides by -8. Remember that when dividing or multiplying an inequality by a negative number, the inequality sign flips:<br />\(x \geq \frac{27}{8}\)<br /><br />So, the solutions are:<br />1. \(x = -\frac{35}{10.78}\)<br />2. \(x \geq -\frac{22}{9}\)<br />3. \(x \geq 12\)<br />4. \(x \geq \frac{27}{8}\)
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